id stringlengths 9 14 | submitter stringlengths 1 50 ⌀ | authors stringlengths 5 666 | title stringlengths 5 242 | comments stringlengths 1 609 ⌀ | journal-ref stringlengths 9 243 ⌀ | doi stringlengths 12 113 ⌀ | report-no stringlengths 2 204 ⌀ | categories stringlengths 6 112 | license stringclasses 9 values | orig_abstract stringlengths 21 2.11k | versions listlengths 1 26 | update_date stringlengths 10 10 | authors_parsed listlengths 1 38 | abstract stringlengths 18 2.11k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
hep-th/9601022 | Arefeva Irina | I.Ya.Aref'eva | Large $N$ Matrix Models and $q$-Deformed Quantum Field Theories | 17 pages, latex. To appear in "From Field Theory to Quantum Groups",
World Scientific. Proceedings to honor J.Lukierski in his 60th birthday | null | 10.1142/9789812830425_0005 | SMI-01-96 | hep-th | null | Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory
for large $N$ is described by q-deformed quantum field. The master fields for
large N theories satisfy to standard equations of relativistic field theory but
fields satisfy $q$-deformed commutation relations with $q=0$. These commutation
relations are realized in the Boltzmannian Fock space. The master field for
gauge theory does not take values in a finite-dimensional Lie algebra however
there is a non-Abelian gauge symmetry. The gauge master field for a subclass of
planar diagrams, so called half-planar diagrams, is also considered. A
recursive set of master fields summing up a matreoshka of 2-particles reducible
planar diagrams is briefly described.
| [
{
"created": "Sun, 7 Jan 1996 16:04:44 GMT",
"version": "v1"
}
] | 2016-11-03 | [
[
"Aref'eva",
"I. Ya.",
""
]
] | Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields satisfy $q$-deformed commutation relations with $q=0$. These commutation relations are realized in the Boltzmannian Fock space. The master field for gauge theory does not take values in a finite-dimensional Lie algebra however there is a non-Abelian gauge symmetry. The gauge master field for a subclass of planar diagrams, so called half-planar diagrams, is also considered. A recursive set of master fields summing up a matreoshka of 2-particles reducible planar diagrams is briefly described. |
1502.07610 | Luis Castro B | Luis B. Castro, Antonio S. de Castro and Pedro Alberto | Pseudospin and spin symmetries in 1+1 dimensions: The case of the
Coulomb potential | 11 pages, 5 figures (Ann. Phys.) | Ann. Phys. (N.Y) 356 (2015) 83 | 10.1016/j.aop.2015.02.033 | null | hep-th math-ph math.MP quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar
Coulomb potential plus a mixing of vector and scalar Coulomb potentials which
have equal or opposite signs is investigated. We explore all the possible signs
of the potentials and discuss their bound-state solutions for fermions and
antifermions. We show the relation between spin and pseudospin symmetries by
means of charge-conjugation and $\gamma^{5}$ chiral transformations. The cases
of pure pseudoscalar and mixed vector-scalar potentials, already analyzed in
previous works, are obtained as particular cases. The results presented can be
extended to 3+1 dimensions.
| [
{
"created": "Thu, 26 Feb 2015 15:59:22 GMT",
"version": "v1"
}
] | 2015-04-09 | [
[
"Castro",
"Luis B.",
""
],
[
"de Castro",
"Antonio S.",
""
],
[
"Alberto",
"Pedro",
""
]
] | The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and $\gamma^{5}$ chiral transformations. The cases of pure pseudoscalar and mixed vector-scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions. |
2303.04479 | Tom\'a\v{s} Brauner | Tomas Brauner, Naoki Yamamoto, Ryo Yokokura | Dipole symmetries from the topology of the phase space and the
constraints on the low-energy spectrum | 32 pages, 2 figures; v2: expanded discussion and updated reference
list; v3: minor revision and further update of the reference list | SciPost Phys. 16, 051 (2024) | 10.21468/SciPostPhys.16.2.051 | KEK-TH-2502 | hep-th cond-mat.str-el | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We demonstrate the general existence of a local dipole conservation law in
bosonic field theory. The scalar charge density arises from the symplectic form
of the system, whereas the tensor current descends from its stress tensor. The
algebra of spatial translations becomes centrally extended in presence of field
configurations with a finite nonzero charge. Furthermore, when the symplectic
form is closed but not exact, the system may, surprisingly, lack a well-defined
momentum density. This leads to a theorem for the presence of additional light
modes in the system whenever the short-distance physics is governed by a
translationally invariant local field theory. We also illustrate this mechanism
for axion electrodynamics as an example of a system with Nambu--Goldstone modes
of higher-form symmetries.
| [
{
"created": "Wed, 8 Mar 2023 09:59:32 GMT",
"version": "v1"
},
{
"created": "Sat, 28 Oct 2023 20:44:08 GMT",
"version": "v2"
},
{
"created": "Thu, 25 Jan 2024 08:01:19 GMT",
"version": "v3"
}
] | 2024-02-21 | [
[
"Brauner",
"Tomas",
""
],
[
"Yamamoto",
"Naoki",
""
],
[
"Yokokura",
"Ryo",
""
]
] | We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu--Goldstone modes of higher-form symmetries. |
hep-th/0205018 | Tomy Scaria | Tomy Scaria, Biswajit Chakraborty | Wigner's little group as a gauge generator in linearized gravity
theories | Latex, 22 pages, no figures, To appear in Class. Quant. Grav | Class.Quant.Grav. 19 (2002) 4445-4462 | 10.1088/0264-9381/19/16/315 | null | hep-th gr-qc | null | We show that the translational subgroup of Wigner's little group for massless
particles in 3+1 dimensions generate gauge transformation in linearized
Einstein gravity. Similarly a suitable representation of the 1-dimensional
translational group T(1) is shown to generate gauge transformation in the
linearized Einstein-Chern-Simons theory in 2+1 dimensions. These
representations are derived systematically from appropriate representations of
translational groups which generate gauge transformations in gauge theories
living in spacetime of one higher dimension by the technique of dimensional
descent. The unified picture thus obtained is compared with a similar picture
available for vector gauge theories in 3+1 and 2+1 dimensions. Finally, the
polarization tensor of Einstein-Pauli-Fierz theory in 2+1 dimensions is shown
to split into the polarization tensors of a pair of Einstein-Chern-Simons
theories with opposite helicities suggesting a doublet structure for
Einstein-Pauli-Fierz theory.
| [
{
"created": "Thu, 2 May 2002 05:08:35 GMT",
"version": "v1"
},
{
"created": "Sat, 13 Jul 2002 06:42:21 GMT",
"version": "v2"
}
] | 2016-09-06 | [
[
"Scaria",
"Tomy",
""
],
[
"Chakraborty",
"Biswajit",
""
]
] | We show that the translational subgroup of Wigner's little group for massless particles in 3+1 dimensions generate gauge transformation in linearized Einstein gravity. Similarly a suitable representation of the 1-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2+1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3+1 and 2+1 dimensions. Finally, the polarization tensor of Einstein-Pauli-Fierz theory in 2+1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for Einstein-Pauli-Fierz theory. |
1009.5414 | Archil Kobakhidze | Archil Kobakhidze | Gravity is not an entropic force | 5 pages, v2: minor corrections; to be published in Physical Review D | Phys.Rev.D83:021502,2011 | 10.1103/PhysRevD.83.021502 | null | hep-th gr-qc hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We argue that experiments with ultra-cold neutrons in the gravitational field
of Earth disprove recent speculations on the entropic origin of gravitation.
| [
{
"created": "Mon, 27 Sep 2010 23:53:35 GMT",
"version": "v1"
},
{
"created": "Thu, 30 Dec 2010 22:04:57 GMT",
"version": "v2"
}
] | 2011-02-01 | [
[
"Kobakhidze",
"Archil",
""
]
] | We argue that experiments with ultra-cold neutrons in the gravitational field of Earth disprove recent speculations on the entropic origin of gravitation. |
hep-th/9709096 | null | Changhyun Ahn, Kyungho Oh, Radu Tatar | M Theory Fivebrane Interpretation for Strong Coupling Dynamics of
SO(N_c) Gauge Theories | 15 pages, Latex, English corrected, Version to Appear in Physics
Letters B | Phys.Lett.B416:75-84,1998 | 10.1016/S0370-2693(97)01311-7 | SNUTP-97-130, UM-TG-201 | hep-th | null | We study M theory fivebranes to understand the moduli space of vacua of N=1
supersymmetric SO(N_c) gauge theory with N_f flavors in four dimensions. We
discuss how the various branches of this theory arise in the string/M theory
brane configurations and compare our results with the ones obtained earlier by
Intriligator and Seiberg in the context of field theory.
In the M theory approach, we explain the various branches from the asymptotic
position of semi-infinite D4 branes in the $w=x^8+i x^9$ direction, which is
closely related to the eigenvalues of the meson matrix $M^{ij} = Q^{i}_a
Q^{j}_a$ where $Q^{i}_a$ is a squark multiplet ( $i=1, \cdots, 2N_f$ and $ a=1,
\cdots, N_c$).In M theory, these branches are explained by observing a new
phenomena which did not occur for the gauge groups SU(N_c) or Sp(N_c).
| [
{
"created": "Mon, 15 Sep 1997 23:53:03 GMT",
"version": "v1"
},
{
"created": "Tue, 16 Sep 1997 01:22:44 GMT",
"version": "v2"
},
{
"created": "Sun, 12 Oct 1997 22:25:45 GMT",
"version": "v3"
}
] | 2014-11-18 | [
[
"Ahn",
"Changhyun",
""
],
[
"Oh",
"Kyungho",
""
],
[
"Tatar",
"Radu",
""
]
] | We study M theory fivebranes to understand the moduli space of vacua of N=1 supersymmetric SO(N_c) gauge theory with N_f flavors in four dimensions. We discuss how the various branches of this theory arise in the string/M theory brane configurations and compare our results with the ones obtained earlier by Intriligator and Seiberg in the context of field theory. In the M theory approach, we explain the various branches from the asymptotic position of semi-infinite D4 branes in the $w=x^8+i x^9$ direction, which is closely related to the eigenvalues of the meson matrix $M^{ij} = Q^{i}_a Q^{j}_a$ where $Q^{i}_a$ is a squark multiplet ( $i=1, \cdots, 2N_f$ and $ a=1, \cdots, N_c$).In M theory, these branches are explained by observing a new phenomena which did not occur for the gauge groups SU(N_c) or Sp(N_c). |
hep-th/9607232 | Jakub Rembielinski | Jakub Rembielinski (Lodz University, Poland) | Tachyons and the preferred frames | 31 pp, LaTeX2e, uses AmS-LaTeX, AmS-symb. To appear in Int. J. Mod.
Phys. A. abstract fixed; the paper remains unchanged | Int.J.Mod.Phys. A12 (1997) 1677-1710 | 10.1142/S0217751X97001122 | null | hep-th hep-ph quant-ph | null | Quantum field theory of space-like particles is investigated in the framework
of absolute causality scheme preserving Lorentz symmetry. It is related to an
appropriate choice of the synchronization procedure (definition of time). In
this formulation existence of field excitations (tachyons) distinguishes an
inertial frame (privileged frame of reference) via spontaneous breaking of the
so called synchronization group. In this scheme relativity principle is broken
but Lorentz symmetry is exactly preserved in agreement with local properties of
the observed world. It is shown that tachyons are associated with unitary
orbits of Poincar\'e mappings induced from $SO(2)$ little group instead of
$SO(2,1)$ one. Therefore the corresponding elementary states are labelled by
helicity. The cases of the helicity $\lambda = 0$ and $\lambda =
\pm\frac{1}{2}$ are investigated in detail and a corresponding consistent field
theory is proposed. In particular, it is shown that the Dirac-like equation
proposed by Chodos et al., inconsistent in the standard formulation of QFT, can
be consistently quantized in the presented framework. This allows us to treat
more seriously possibility that neutrinos might be fermionic tachyons as it is
suggested by experimental data about neutrino masses.
| [
{
"created": "Tue, 30 Jul 1996 22:16:36 GMT",
"version": "v1"
},
{
"created": "Thu, 1 Aug 1996 17:13:10 GMT",
"version": "v2"
}
] | 2009-10-30 | [
[
"Rembielinski",
"Jakub",
"",
"Lodz University, Poland"
]
] | Quantum field theory of space-like particles is investigated in the framework of absolute causality scheme preserving Lorentz symmetry. It is related to an appropriate choice of the synchronization procedure (definition of time). In this formulation existence of field excitations (tachyons) distinguishes an inertial frame (privileged frame of reference) via spontaneous breaking of the so called synchronization group. In this scheme relativity principle is broken but Lorentz symmetry is exactly preserved in agreement with local properties of the observed world. It is shown that tachyons are associated with unitary orbits of Poincar\'e mappings induced from $SO(2)$ little group instead of $SO(2,1)$ one. Therefore the corresponding elementary states are labelled by helicity. The cases of the helicity $\lambda = 0$ and $\lambda = \pm\frac{1}{2}$ are investigated in detail and a corresponding consistent field theory is proposed. In particular, it is shown that the Dirac-like equation proposed by Chodos et al., inconsistent in the standard formulation of QFT, can be consistently quantized in the presented framework. This allows us to treat more seriously possibility that neutrinos might be fermionic tachyons as it is suggested by experimental data about neutrino masses. |
hep-th/9805027 | David Daegene Song | David D. Song and Richard J. Szabo (Oxford) | Black String Entropy from Anomalous D-brane Couplings | 12 pages, LaTeX; Corrections and clarifying comments added | Eur.Phys.J.C13:641-646,2000 | 10.1007/s100520050722 | OUTP-98-32P | hep-th gr-qc | null | The quantum corrections to the counting of statistical entropy for the
5+1-dimensional extremal black string in type-IIB supergravity with two
observers are studied using anomalous Wess-Zumino actions for the corresponding
intersecting D-brane description. The electric-magnetic duality symmetry of the
anomalous theory implies a new symmetry between D-string and D-fivebrane
sources and renders opposite sign for the RR charge of one of the intersecting
D-branes relative to that of the black string. The electric-magnetic symmetric
Hilbert space decomposes into subspaces associated with interior and exterior
regions and it is shown that, for an outside observer, the expectation value of
a horizon area operator agrees with the deviation of the classical horizon area
in going from extremal to near-extremal black strings.
| [
{
"created": "Tue, 5 May 1998 22:29:42 GMT",
"version": "v1"
},
{
"created": "Wed, 22 Jul 1998 20:54:26 GMT",
"version": "v2"
},
{
"created": "Wed, 9 Sep 1998 00:08:30 GMT",
"version": "v3"
}
] | 2011-09-13 | [
[
"Song",
"David D.",
"",
"Oxford"
],
[
"Szabo",
"Richard J.",
"",
"Oxford"
]
] | The quantum corrections to the counting of statistical entropy for the 5+1-dimensional extremal black string in type-IIB supergravity with two observers are studied using anomalous Wess-Zumino actions for the corresponding intersecting D-brane description. The electric-magnetic duality symmetry of the anomalous theory implies a new symmetry between D-string and D-fivebrane sources and renders opposite sign for the RR charge of one of the intersecting D-branes relative to that of the black string. The electric-magnetic symmetric Hilbert space decomposes into subspaces associated with interior and exterior regions and it is shown that, for an outside observer, the expectation value of a horizon area operator agrees with the deviation of the classical horizon area in going from extremal to near-extremal black strings. |
hep-th/9911203 | Sheikh-Jabbari Mohammad | M.M. Sheikh-Jabbari | A Note on T-Duality, Open Strings in B-field Background and Canonical
Transformations | Tex File, 6 Pages, no figures | Phys.Lett.B474:292-294,2000 | 10.1016/S0370-2693(00)00030-7 | IC/99/179 | hep-th | null | In this paper we study T-duality for open strings ending on branes with
non-zero B-field on them from the point of view of canonical transformations.
For the particular case of type II strings on the two torus we show that the
$Sl(2,Z)_N$ transformations can be understood as a sub-class of canonical
transformations on the open strings in the B-field background.
| [
{
"created": "Thu, 25 Nov 1999 11:49:36 GMT",
"version": "v1"
}
] | 2009-10-07 | [
[
"Sheikh-Jabbari",
"M. M.",
""
]
] | In this paper we study T-duality for open strings ending on branes with non-zero B-field on them from the point of view of canonical transformations. For the particular case of type II strings on the two torus we show that the $Sl(2,Z)_N$ transformations can be understood as a sub-class of canonical transformations on the open strings in the B-field background. |
hep-th/0412040 | James Cline | N. Barnaby, C.P. Burgess, J.M. Cline | Warped Reheating in Brane-Antibrane Inflation | 23 pages, 5 figures; new section on tunneling added; fixed typo | JCAP0504:007,2005 | 10.1088/1475-7516/2005/04/007 | null | hep-th hep-ph | null | We examine how reheating occurs after brane-antibrane inflation in warped
geometries, such as those which have recently been considered for Type IIB
string vacua. We adopt the standard picture that the energy released by brane
annihilation is dominantly dumped into massive bulk (closed-string) modes which
eventually cascade down into massless particles, but argue that the this need
not mean that the result is mostly gravitons with negligible visible radiation
on the Standard Model brane. We show that if the inflationary throat is not too
strongly warped, and if the string coupling is sufficiently weak, then a
significant fraction of the energy density from annihilation will be deposited
on the Standard Model brane, even if it is separated from the inflationary
throat by being in some more deeply warped throat. This is due to the
exponential growth of the massive Kaluza-Klein wave functions toward the
infrared ends of the throats. We argue that the possibility of this process
removes a conceptual obstacle to the construction of multi-throat models,
wherein inflation occurs in a different throat than the one in which the
Standard Model brane resides. Such multi-throat models are desirable because
they can help to reconcile the scale of inflation with the supersymmetry
breaking scale on the Standard Model brane, and because they can allow cosmic
strings to be sufficiently long-lived to be observable during the present
epoch.
| [
{
"created": "Fri, 3 Dec 2004 16:06:46 GMT",
"version": "v1"
},
{
"created": "Wed, 8 Jun 2005 03:41:46 GMT",
"version": "v2"
},
{
"created": "Wed, 15 Jun 2005 11:36:38 GMT",
"version": "v3"
}
] | 2008-11-26 | [
[
"Barnaby",
"N.",
""
],
[
"Burgess",
"C. P.",
""
],
[
"Cline",
"J. M.",
""
]
] | We examine how reheating occurs after brane-antibrane inflation in warped geometries, such as those which have recently been considered for Type IIB string vacua. We adopt the standard picture that the energy released by brane annihilation is dominantly dumped into massive bulk (closed-string) modes which eventually cascade down into massless particles, but argue that the this need not mean that the result is mostly gravitons with negligible visible radiation on the Standard Model brane. We show that if the inflationary throat is not too strongly warped, and if the string coupling is sufficiently weak, then a significant fraction of the energy density from annihilation will be deposited on the Standard Model brane, even if it is separated from the inflationary throat by being in some more deeply warped throat. This is due to the exponential growth of the massive Kaluza-Klein wave functions toward the infrared ends of the throats. We argue that the possibility of this process removes a conceptual obstacle to the construction of multi-throat models, wherein inflation occurs in a different throat than the one in which the Standard Model brane resides. Such multi-throat models are desirable because they can help to reconcile the scale of inflation with the supersymmetry breaking scale on the Standard Model brane, and because they can allow cosmic strings to be sufficiently long-lived to be observable during the present epoch. |
1410.8148 | Jos\'e Alejandro Rosabal Rodr\'iguez | J.A. Rosabal | On the exceptional generalised Lie derivative for $d\geq7$ | Version accepted to JHEP | null | 10.1007/JHEP09(2015)153 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this work we revisit the $E_8\times\mathbb{R}^{+}$ generalised Lie
derivative encoding the algebra of diffeomorphisms and gauge transformations of
compactifications of M-theory on eight-dimensional manifolds, by extending
certain features of the $E_7\times\mathbb{R}^{+}$ one. Compared to its
$E_d\times\mathbb{R}^{+},\ d\le 7$ counterparts, a new term is needed for
consistency. However, we find that no compensating parameters need to be
introduced, but rather that the new term can be written in terms of the
ordinary generalised gauge parameters by means of a connection. This implies
that no further degrees of freedom, beyond those of the field content of the
$E_{8}$ group, are needed to have a well defined theory. We discuss the
implications of the structure of the $E_8\times\mathbb{R}^{+}$ generalised
transformation on the construction of the $d=8$ generalised geometry. Finally,
we suggest how to lift the generalised Lie derivative to eleven dimensions.
| [
{
"created": "Wed, 29 Oct 2014 20:04:11 GMT",
"version": "v1"
},
{
"created": "Wed, 16 Sep 2015 19:09:28 GMT",
"version": "v2"
}
] | 2015-10-28 | [
[
"Rosabal",
"J. A.",
""
]
] | In this work we revisit the $E_8\times\mathbb{R}^{+}$ generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the $E_7\times\mathbb{R}^{+}$ one. Compared to its $E_d\times\mathbb{R}^{+},\ d\le 7$ counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the $E_{8}$ group, are needed to have a well defined theory. We discuss the implications of the structure of the $E_8\times\mathbb{R}^{+}$ generalised transformation on the construction of the $d=8$ generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions. |
hep-th/9507084 | Ilinski Kirill N. | A.V.Ilinskaia and K.N.Ilinski | Generalization of Agranovich-Toshich transformation and constraint free
bosonic representation for systems of truncated oscillators | latex, 8 pages, no figures | J.Phys. A29 (1996) L23-L30 | 10.1088/0305-4470/29/2/001 | TPBU-95-7 | hep-th cond-mat | null | The generalization of Agranovich-Toshich representation of paulion operators
in terms of bosonic ones for the case of truncated oscillators of higher ranks
is represented. We use this generalization to introduce a new constraint free
bosonic description of truncated oscillator systems. The corresponding
functional integral representations for thermodynamic quantities are given and
the application to investigations of Long Rang Order in the system is
discussed.
| [
{
"created": "Sun, 16 Jul 1995 10:49:43 GMT",
"version": "v1"
}
] | 2009-10-28 | [
[
"Ilinskaia",
"A. V.",
""
],
[
"Ilinski",
"K. N.",
""
]
] | The generalization of Agranovich-Toshich representation of paulion operators in terms of bosonic ones for the case of truncated oscillators of higher ranks is represented. We use this generalization to introduce a new constraint free bosonic description of truncated oscillator systems. The corresponding functional integral representations for thermodynamic quantities are given and the application to investigations of Long Rang Order in the system is discussed. |
hep-th/0004183 | Chong-Sun Chu | Chong-Sun Chu, Rodolfo Russo, Stefano Sciuto | Multiloop String Amplitudes with B-Field and Noncommutative QFT | Latex. 27 pages. 9 figures v2: typos corrected, references added; v3:
ref. added, version to appear in NPB | Nucl.Phys.B585:193-218,2000 | 10.1016/S0550-3213(00)00388-6 | null | hep-th | null | The multiloop amplitudes for the bosonic string in presence of a constant
B-field are built by using the basic commutation relations for the open string
zero modes and oscillators. The open string Green function on the annulus is
obtained from the one loop scattering amplitude among N tachyons. For higher
loops, it is necessary to use the so called three Reggeon vertex, which
describes the emission from the open string of another string and not simply of
a tachyon. We find that the modifications to the three (and multi) Reggeon
vertex due to the B-field only affect the zero modes and can be written in a
simple and elegant way. Therefore we can easily sew these vertices together and
write the general expression for the multiloop N-Reggeon vertex, which contains
any loop string amplitude, in presence of the B-field. The field theory limit
is also considered in some examples at two loops and reproduces exactly the
results of a noncommutative scalar field theory.
| [
{
"created": "Wed, 26 Apr 2000 18:33:58 GMT",
"version": "v1"
},
{
"created": "Fri, 5 May 2000 17:30:52 GMT",
"version": "v2"
},
{
"created": "Mon, 24 Jul 2000 14:19:57 GMT",
"version": "v3"
}
] | 2011-07-19 | [
[
"Chu",
"Chong-Sun",
""
],
[
"Russo",
"Rodolfo",
""
],
[
"Sciuto",
"Stefano",
""
]
] | The multiloop amplitudes for the bosonic string in presence of a constant B-field are built by using the basic commutation relations for the open string zero modes and oscillators. The open string Green function on the annulus is obtained from the one loop scattering amplitude among N tachyons. For higher loops, it is necessary to use the so called three Reggeon vertex, which describes the emission from the open string of another string and not simply of a tachyon. We find that the modifications to the three (and multi) Reggeon vertex due to the B-field only affect the zero modes and can be written in a simple and elegant way. Therefore we can easily sew these vertices together and write the general expression for the multiloop N-Reggeon vertex, which contains any loop string amplitude, in presence of the B-field. The field theory limit is also considered in some examples at two loops and reproduces exactly the results of a noncommutative scalar field theory. |
1609.04351 | Sang-A Park | Seungjoon Hyun, Sang-A Park, Sang-Heon Yi | Revisit to Thermodynamic Relations in the AdS/CMT Models | 1+18 pages, plain LaTeX; v2 typo fixed and references added; v3
version to appear in PRD | Phys. Rev. D 95, 066012 (2017) | 10.1103/PhysRevD.95.066012 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Motivated by the recent unified approach to the Smarr-like relation of AdS
planar black holes in conjunction with the quasi-local formalism on conserved
charges, we revisit the quantum statistical and thermodynamic relations of
hairy AdS planar black holes. By extending the previous results, we identify
the hairy contribution in the bulk and show that the holographic computation
can be improved so that it is consistent with the bulk computation. We argue
that the first law can be retained in its universal form while the relation
between the on-shell renormalized Euclidean action and its free energy
interpretation in gravity may be deformed to contain the hairy contribution in
hairy AdS black holes.
| [
{
"created": "Wed, 14 Sep 2016 17:14:30 GMT",
"version": "v1"
},
{
"created": "Thu, 22 Sep 2016 08:26:05 GMT",
"version": "v2"
},
{
"created": "Fri, 3 Mar 2017 06:07:26 GMT",
"version": "v3"
}
] | 2017-03-29 | [
[
"Hyun",
"Seungjoon",
""
],
[
"Park",
"Sang-A",
""
],
[
"Yi",
"Sang-Heon",
""
]
] | Motivated by the recent unified approach to the Smarr-like relation of AdS planar black holes in conjunction with the quasi-local formalism on conserved charges, we revisit the quantum statistical and thermodynamic relations of hairy AdS planar black holes. By extending the previous results, we identify the hairy contribution in the bulk and show that the holographic computation can be improved so that it is consistent with the bulk computation. We argue that the first law can be retained in its universal form while the relation between the on-shell renormalized Euclidean action and its free energy interpretation in gravity may be deformed to contain the hairy contribution in hairy AdS black holes. |
2403.05875 | Long Zhao | Song He, Pak Hang Chris Lau, Long Zhao | Detecting quantum chaos via pseudo-entropy and negativity | 31 pages, 12 figures | null | null | null | hep-th cond-mat.dis-nn | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Quantum informatic quantities such as entanglement entropy are useful in
detecting quantum phase transitions. Recently, a new entanglement measure
called pseudo-entropy was proposed which is a generalization of the more
well-known entanglement entropy. It has many nice properties and is useful in
the study of post-selection measurements. In this paper, one of our goals is to
explore the properties of pseudo-entropy and study the effectiveness of it as a
quantum chaos diagnostic, i.e. as a tool to distinguish between chaotic and
integrable systems. Using various variants of the SYK model, we study the
signal of quantum chaos captured in the pseudo-entropy and relate it to the
spectral form factor (SFF) and local operator entanglement (LOE). We also
explore another quantity called the negativity of entanglement which is a
useful entanglement measure for a mixed state. We generalized it to accommodate
the transition matrix and called it pseudo-negativity in analogy to
pseudo-entropy. We found that it also nicely captures the spectral properties
of a chaotic system and hence also plays a role as a tool of quantum chaos
diagnostic.
| [
{
"created": "Sat, 9 Mar 2024 10:57:13 GMT",
"version": "v1"
}
] | 2024-03-12 | [
[
"He",
"Song",
""
],
[
"Lau",
"Pak Hang Chris",
""
],
[
"Zhao",
"Long",
""
]
] | Quantum informatic quantities such as entanglement entropy are useful in detecting quantum phase transitions. Recently, a new entanglement measure called pseudo-entropy was proposed which is a generalization of the more well-known entanglement entropy. It has many nice properties and is useful in the study of post-selection measurements. In this paper, one of our goals is to explore the properties of pseudo-entropy and study the effectiveness of it as a quantum chaos diagnostic, i.e. as a tool to distinguish between chaotic and integrable systems. Using various variants of the SYK model, we study the signal of quantum chaos captured in the pseudo-entropy and relate it to the spectral form factor (SFF) and local operator entanglement (LOE). We also explore another quantity called the negativity of entanglement which is a useful entanglement measure for a mixed state. We generalized it to accommodate the transition matrix and called it pseudo-negativity in analogy to pseudo-entropy. We found that it also nicely captures the spectral properties of a chaotic system and hence also plays a role as a tool of quantum chaos diagnostic. |
2004.14387 | Pavel Putrov | Atish Dabholkar, Pavel Putrov, Edward Witten | Duality and Mock Modularity | 50 pages, 1 figure; v2: misprints corrected, clarifications added in
Section 5.1; v3: minor clarifications added | SciPost Phys. 9, 072 (2020) | 10.21468/SciPostPhys.9.5.072 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We derive a holomorphic anomaly equation for the Vafa-Witten partition
function for twisted four-dimensional $\mathcal{N} =4$ super Yang-Mills theory
on $\mathbb{CP}^{2}$ for the gauge group $SO(3)$ from the path integral of the
effective theory on the Coulomb branch. The holomorphic kernel of this
equation, which receives contributions only from the instantons, is not modular
but `mock modular'. The partition function has correct modular properties
expected from $S$-duality only after including the anomalous nonholomorphic
boundary contributions from anti-instantons. Using M-theory duality, we relate
this phenomenon to the holomorphic anomaly of the elliptic genus of a
two-dimensional noncompact sigma model and compute it independently in two
dimensions. The anomaly both in four and in two dimensions can be traced to a
topological term in the effective action of six-dimensional (2,0) theory on the
tensor branch. We consider generalizations to other manifolds and other gauge
groups to show that mock modularity is generic and essential for exhibiting
duality when the relevant field space is noncompact.
| [
{
"created": "Wed, 29 Apr 2020 18:00:00 GMT",
"version": "v1"
},
{
"created": "Tue, 16 Jun 2020 17:41:37 GMT",
"version": "v2"
},
{
"created": "Tue, 20 Oct 2020 10:40:36 GMT",
"version": "v3"
}
] | 2020-11-18 | [
[
"Dabholkar",
"Atish",
""
],
[
"Putrov",
"Pavel",
""
],
[
"Witten",
"Edward",
""
]
] | We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional $\mathcal{N} =4$ super Yang-Mills theory on $\mathbb{CP}^{2}$ for the gauge group $SO(3)$ from the path integral of the effective theory on the Coulomb branch. The holomorphic kernel of this equation, which receives contributions only from the instantons, is not modular but `mock modular'. The partition function has correct modular properties expected from $S$-duality only after including the anomalous nonholomorphic boundary contributions from anti-instantons. Using M-theory duality, we relate this phenomenon to the holomorphic anomaly of the elliptic genus of a two-dimensional noncompact sigma model and compute it independently in two dimensions. The anomaly both in four and in two dimensions can be traced to a topological term in the effective action of six-dimensional (2,0) theory on the tensor branch. We consider generalizations to other manifolds and other gauge groups to show that mock modularity is generic and essential for exhibiting duality when the relevant field space is noncompact. |
1505.05092 | Blaise Gout\'eraux | Richard A. Davison and Blaise Gout\'eraux | Dissecting holographic conductivities | v2: minor edits, matches published version. v1: 26 pages, 1 figure | JHEP 1509 (2015) 090 | 10.1007/JHEP09(2015)090 | SU-ITP-15/12 | hep-th cond-mat.str-el gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The DC thermoelectric conductivities of holographic systems in which
translational symmetry is broken can be efficiently computed in terms of the
near-horizon data of the dual black hole. By calculating the frequency
dependent conductivities to the first subleading order in the momentum
relaxation rate, we give a physical explanation for these conductivities in the
simplest such example, in the limit of slow momentum relaxation. Specifically,
we decompose each conductivity into the sum of a coherent contribution due to
momentum relaxation and an incoherent contribution, due to intrinsic current
relaxation. This decomposition is different from those previously proposed, and
is consistent with the known hydrodynamic properties in the translationally
invariant limit. This is the first step towards constructing a consistent
theory of charged hydrodynamics with slow momentum relaxation.
| [
{
"created": "Tue, 19 May 2015 17:25:00 GMT",
"version": "v1"
},
{
"created": "Tue, 15 Sep 2015 16:58:26 GMT",
"version": "v2"
}
] | 2015-09-24 | [
[
"Davison",
"Richard A.",
""
],
[
"Goutéraux",
"Blaise",
""
]
] | The DC thermoelectric conductivities of holographic systems in which translational symmetry is broken can be efficiently computed in terms of the near-horizon data of the dual black hole. By calculating the frequency dependent conductivities to the first subleading order in the momentum relaxation rate, we give a physical explanation for these conductivities in the simplest such example, in the limit of slow momentum relaxation. Specifically, we decompose each conductivity into the sum of a coherent contribution due to momentum relaxation and an incoherent contribution, due to intrinsic current relaxation. This decomposition is different from those previously proposed, and is consistent with the known hydrodynamic properties in the translationally invariant limit. This is the first step towards constructing a consistent theory of charged hydrodynamics with slow momentum relaxation. |
0706.0744 | Thomas Quella | Thomas Quella, Volker Schomerus | Free fermion resolution of supergroup WZNW models | 47 pages | JHEP 0709:085,2007 | 10.1088/1126-6708/2007/09/085 | DESY 07-074, KCL-MTH-07-06, NSF-KITP-07-128 | hep-th cond-mat.stat-mech math-ph math.MP math.QA math.RT | null | Extending our earlier work on PSL(2|2), we explain how to reduce the solution
of WZNW models on general type I supergroups to those defined on the bosonic
subgroup. The new analysis covers in particular the supergroups GL(M|N) along
with several close relatives such as PSL(N|N), certain Poincare supergroups and
the series OSP(2|2N). This remarkable progress relies on the use of a special
Feigin-Fuchs type representation. In preparation for the field theory analysis,
we shall exploit a minisuperspace analogue of a free fermion construction to
deduce the spectrum of the Laplacian on type I supergroups. The latter is shown
to be non-diagonalizable. After lifting these results to the full WZNW model,
we address various issues of the field theory, including its modular invariance
and the computation of correlation functions. In agreement with previous
findings, supergroup WZNW models allow to study chiral and non-chiral aspects
of logarithmic conformal field theory within a geometric framework. We shall
briefly indicate how insights from WZNW models carry over to non-geometric
examples, such as e.g. the W(p) triplet models.
| [
{
"created": "Wed, 6 Jun 2007 13:28:04 GMT",
"version": "v1"
}
] | 2009-04-17 | [
[
"Quella",
"Thomas",
""
],
[
"Schomerus",
"Volker",
""
]
] | Extending our earlier work on PSL(2|2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M|N) along with several close relatives such as PSL(N|N), certain Poincare supergroups and the series OSP(2|2N). This remarkable progress relies on the use of a special Feigin-Fuchs type representation. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of a free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models. |
2405.09614 | Borna Salehian | Paolo Creminelli, Oliver Janssen, Borna Salehian, Leonardo Senatore | Positivity bounds on electromagnetic properties of media | 27 pages + appendices, 7 figures | null | null | null | hep-th cond-mat.stat-mech cond-mat.str-el | http://creativecommons.org/licenses/by/4.0/ | We study the constraints imposed on the electromagnetic response of general
media by microcausality (commutators of local fields vanish outside the light
cone) and positivity of the imaginary parts (the medium can only absorb energy
from the external field). The equations of motion for the average
electromagnetic field in a medium -- the macroscopic Maxwell equations -- can
be derived from the in-in effective action and the effect of the medium is
encoded in the electric and magnetic permeabilities
$\varepsilon(\omega,|\boldsymbol{k}|)$ and $\mu(\omega,|\boldsymbol{k}|)$.
Microcausality implies analyticity of the retarded Green's functions when the
imaginary part of the $4$-vector $(\omega,\boldsymbol{k})$ lies in forward
light cone. With appropriate assumptions about the behavior of the medium at
high frequencies one derives dispersion relations, originally studied by
Leontovich. In the case of dielectrics these relations, combined with the
positivity of the imaginary parts, imply bounds on the low-energy values of the
response, $\varepsilon(0,0)$ and $\mu(0,0)$. In particular the quantities
$\varepsilon(0,0)-1$ and $\varepsilon(0,0) - 1/\mu(0,0)$ are constrained to be
positive and equal to integrals over the imaginary parts of the response. We
discuss various improvements of these bounds in the case of non-relativistic
media and with additional assumptions about the UV behavior.
| [
{
"created": "Wed, 15 May 2024 18:00:02 GMT",
"version": "v1"
}
] | 2024-05-17 | [
[
"Creminelli",
"Paolo",
""
],
[
"Janssen",
"Oliver",
""
],
[
"Salehian",
"Borna",
""
],
[
"Senatore",
"Leonardo",
""
]
] | We study the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from the external field). The equations of motion for the average electromagnetic field in a medium -- the macroscopic Maxwell equations -- can be derived from the in-in effective action and the effect of the medium is encoded in the electric and magnetic permeabilities $\varepsilon(\omega,|\boldsymbol{k}|)$ and $\mu(\omega,|\boldsymbol{k}|)$. Microcausality implies analyticity of the retarded Green's functions when the imaginary part of the $4$-vector $(\omega,\boldsymbol{k})$ lies in forward light cone. With appropriate assumptions about the behavior of the medium at high frequencies one derives dispersion relations, originally studied by Leontovich. In the case of dielectrics these relations, combined with the positivity of the imaginary parts, imply bounds on the low-energy values of the response, $\varepsilon(0,0)$ and $\mu(0,0)$. In particular the quantities $\varepsilon(0,0)-1$ and $\varepsilon(0,0) - 1/\mu(0,0)$ are constrained to be positive and equal to integrals over the imaginary parts of the response. We discuss various improvements of these bounds in the case of non-relativistic media and with additional assumptions about the UV behavior. |
1901.09872 | Marco Garofalo | Stefano Capitani, Petros Dimopoulos, Roberto Frezzotti, Marco
Garofalo, Bartosz Kostrzewa, Ferenc Pittler, Giancarlo Rossi, Carsten Urbach | Dynamical Generation of Elementary Fermion Mass: First Lattice Evidence | 24 pages, 17 figures | Phys. Rev. Lett. 123, 061802 (2019) | 10.1103/PhysRevLett.123.061802 | null | hep-th hep-lat hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Using lattice simulations we demonstrate from first principles the existence
of a non-perturbative mechanism for elementary particle mass generation in
models with gauge fields, fermions and scalars, if an exact invariance forbids
power divergent fermion masses and fermionic chiral symmetries broken at UV
scale are maximally restored. We show that in the Nambu-Goldstone phase a
fermion mass term, unrelated to the Yukawa operator, is dynamically generated.
In models with electro-weak interactions weak boson masses are also generated
opening new scenarios for beyond the Standard Model physics.
| [
{
"created": "Mon, 28 Jan 2019 18:26:44 GMT",
"version": "v1"
},
{
"created": "Tue, 27 Aug 2019 15:06:20 GMT",
"version": "v2"
}
] | 2019-08-28 | [
[
"Capitani",
"Stefano",
""
],
[
"Dimopoulos",
"Petros",
""
],
[
"Frezzotti",
"Roberto",
""
],
[
"Garofalo",
"Marco",
""
],
[
"Kostrzewa",
"Bartosz",
""
],
[
"Pittler",
"Ferenc",
""
],
[
"Rossi",
"Giancarlo",
""
],
[
"Urbach",
"Carsten",
""
]
] | Using lattice simulations we demonstrate from first principles the existence of a non-perturbative mechanism for elementary particle mass generation in models with gauge fields, fermions and scalars, if an exact invariance forbids power divergent fermion masses and fermionic chiral symmetries broken at UV scale are maximally restored. We show that in the Nambu-Goldstone phase a fermion mass term, unrelated to the Yukawa operator, is dynamically generated. In models with electro-weak interactions weak boson masses are also generated opening new scenarios for beyond the Standard Model physics. |
hep-th/0702012 | Xi Yin | Davide Gaiotto, Xi Yin | Examples of M5-Brane Elliptic Genera | 13 pages | JHEP 0711:004,2007 | 10.1088/1126-6708/2007/11/004 | null | hep-th | null | We determine the modified elliptic genus of an M5-brane wrapped on various
one modulus Calabi-Yau spaces, using modular invariance together with some
known Gopakumar-Vafa invariants of small degrees. As a bonus, we find
nontrivial relations among Gopakumar-Vafa invariants of different degrees and
genera from modular invariance.
| [
{
"created": "Thu, 1 Feb 2007 20:49:01 GMT",
"version": "v1"
}
] | 2009-04-22 | [
[
"Gaiotto",
"Davide",
""
],
[
"Yin",
"Xi",
""
]
] | We determine the modified elliptic genus of an M5-brane wrapped on various one modulus Calabi-Yau spaces, using modular invariance together with some known Gopakumar-Vafa invariants of small degrees. As a bonus, we find nontrivial relations among Gopakumar-Vafa invariants of different degrees and genera from modular invariance. |
2404.15077 | Robert Saskowski | Evan Deddo, James T. Liu, Leopoldo A. Pando Zayas, Robert J. Saskowski | Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG
Flows | 27 pages, 3 figures; references added | null | null | LCTP-24-07 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We revisit the existence of monotonic quantities along renormalization group
flows using only the Null Energy Condition and the Ryu-Takayanagi formula for
the entanglement entropy of field theories with anti-de Sitter gravity duals.
In particular, we consider flows within the same dimension and holographically
reprove the $c$-, $F$-, and $a$-theorems in dimensions two, three, and four. We
focus on the family of maximally spherical entangling surfaces, define a
quasi-constant of motion corresponding to the breaking of conformal invariance,
and use a properly defined distance between minimal surfaces to construct a
holographic $c$-function that is monotonic along the flow. We then apply our
method to the case of flows across dimensions: There, we reprove the
monotonicity of flows from $\mathrm{AdS}_{D+1}$ to $\mathrm{AdS}_3$ and prove
the novel case of flows from $\mathrm{AdS}_5$ to $\mathrm{AdS}_4$.
| [
{
"created": "Tue, 23 Apr 2024 14:25:39 GMT",
"version": "v1"
},
{
"created": "Fri, 24 May 2024 14:20:17 GMT",
"version": "v2"
}
] | 2024-05-27 | [
[
"Deddo",
"Evan",
""
],
[
"Liu",
"James T.",
""
],
[
"Zayas",
"Leopoldo A. Pando",
""
],
[
"Saskowski",
"Robert J.",
""
]
] | We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the $c$-, $F$-, and $a$-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a holographic $c$-function that is monotonic along the flow. We then apply our method to the case of flows across dimensions: There, we reprove the monotonicity of flows from $\mathrm{AdS}_{D+1}$ to $\mathrm{AdS}_3$ and prove the novel case of flows from $\mathrm{AdS}_5$ to $\mathrm{AdS}_4$. |
2403.00073 | Florian Ecker | Ankit Aggarwal, Florian Ecker, Daniel Grumiller, Dmitri Vassilevich | Carroll Hawking effect | 5 pages, v2: added refs | null | null | TUW-24-02 | hep-th | http://creativecommons.org/licenses/by/4.0/ | Carroll black holes with an associated Carroll temperature were introduced
recently. So far, it is unclear if they exhibit a Hawking-like effect. To solve
this, we study scalar fields on Carroll black hole backgrounds. Inspired by
anomaly methods, we derive a Hawking-like energy-momentum tensor compatible
with the Carroll temperature and the Stefan-Boltzmann law. Key steps in our
derivation are the finiteness of energy at the Carroll extremal surface and
compatibility with the Carroll Ward identities, thereby eliminating,
respectively, the Carroll-analogs of the Boulware and Unruh vacua.
| [
{
"created": "Thu, 29 Feb 2024 19:02:56 GMT",
"version": "v1"
},
{
"created": "Wed, 13 Mar 2024 20:43:47 GMT",
"version": "v2"
}
] | 2024-03-15 | [
[
"Aggarwal",
"Ankit",
""
],
[
"Ecker",
"Florian",
""
],
[
"Grumiller",
"Daniel",
""
],
[
"Vassilevich",
"Dmitri",
""
]
] | Carroll black holes with an associated Carroll temperature were introduced recently. So far, it is unclear if they exhibit a Hawking-like effect. To solve this, we study scalar fields on Carroll black hole backgrounds. Inspired by anomaly methods, we derive a Hawking-like energy-momentum tensor compatible with the Carroll temperature and the Stefan-Boltzmann law. Key steps in our derivation are the finiteness of energy at the Carroll extremal surface and compatibility with the Carroll Ward identities, thereby eliminating, respectively, the Carroll-analogs of the Boulware and Unruh vacua. |
2305.15440 | Joel Karlsson | Thomas Hertog, Oliver Janssen and Joel Karlsson | The Kontsevich-Segal Criterion in the No-Boundary State Constrains
Inflation | Dedicated to the memory of Jim Hartle | Phys. Rev. Lett. 131, 191501 (2023) | 10.1103/PhysRevLett.131.191501 | null | hep-th gr-qc | http://creativecommons.org/licenses/by/4.0/ | We show that the Kontsevich-Segal (KS) criterion, applied to the complex
saddles that specify the semiclassical no-boundary wave function, acts as a
selection mechanism on inflationary scalar field potentials. Completing the
observable phase of slow-roll inflation with a no-boundary origin, the KS
criterion effectively bounds the tensor-to-scalar ratio of cosmic microwave
background fluctuations to be less than 0.08, in line with current
observations. We trace the failure of complex saddles to meet the KS criterion
to the development of a tachyon in their spectrum of perturbations.
| [
{
"created": "Tue, 23 May 2023 20:03:34 GMT",
"version": "v1"
},
{
"created": "Thu, 9 Nov 2023 18:54:34 GMT",
"version": "v2"
}
] | 2023-11-10 | [
[
"Hertog",
"Thomas",
""
],
[
"Janssen",
"Oliver",
""
],
[
"Karlsson",
"Joel",
""
]
] | We show that the Kontsevich-Segal (KS) criterion, applied to the complex saddles that specify the semiclassical no-boundary wave function, acts as a selection mechanism on inflationary scalar field potentials. Completing the observable phase of slow-roll inflation with a no-boundary origin, the KS criterion effectively bounds the tensor-to-scalar ratio of cosmic microwave background fluctuations to be less than 0.08, in line with current observations. We trace the failure of complex saddles to meet the KS criterion to the development of a tachyon in their spectrum of perturbations. |
2207.02172 | Nicol\`o Petri | Giuseppe Dibitetto, Nicol\`o Petri | Searching for Coleman-de Luccia bubbles in AdS compactifications | 29 pages, 6 figures, 1 appendix. v2: Added references | null | 10.1103/PhysRevD.107.046020 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Coleman-de Luccia transitions are spontaneous processes of nucleation of
bubbles within metastable gravitational vacua including in their interior a
true stable vacuum. From the perspective of lower-dimensional gauged
supergravities obtained by truncating Type II and M-theory, these instantonic
processes are represented by smooth domain walls featured by de Sitter
foliations. These geometries must connect two different AdS vacua in such a way
that the wall is defined by an interior and an exterior. We propose a
first-order formulation for such radial flows and present two fully backreacted
examples of gravitational instantons obtained through this technique, beyond
the thin-wall approximation. In the first we consider minimal 7d supergravity
describing the truncation of M-theory over a squashed 4-sphere and admitting
two AdS$_7$ vacua, one supersymmetric and the other not. Secondly we apply the
same strategy to 6d Romans supergravity obtained with consistent truncation of
massive IIA supergravity. Also in this case we derive a dS domain wall
interpolating between the Brandhuber-Oz vacuum and the non-supersymmetric
AdS$_6$ vacuum of the theory.
| [
{
"created": "Tue, 5 Jul 2022 17:00:31 GMT",
"version": "v1"
},
{
"created": "Mon, 16 Jan 2023 14:15:48 GMT",
"version": "v2"
}
] | 2023-03-08 | [
[
"Dibitetto",
"Giuseppe",
""
],
[
"Petri",
"Nicolò",
""
]
] | Coleman-de Luccia transitions are spontaneous processes of nucleation of bubbles within metastable gravitational vacua including in their interior a true stable vacuum. From the perspective of lower-dimensional gauged supergravities obtained by truncating Type II and M-theory, these instantonic processes are represented by smooth domain walls featured by de Sitter foliations. These geometries must connect two different AdS vacua in such a way that the wall is defined by an interior and an exterior. We propose a first-order formulation for such radial flows and present two fully backreacted examples of gravitational instantons obtained through this technique, beyond the thin-wall approximation. In the first we consider minimal 7d supergravity describing the truncation of M-theory over a squashed 4-sphere and admitting two AdS$_7$ vacua, one supersymmetric and the other not. Secondly we apply the same strategy to 6d Romans supergravity obtained with consistent truncation of massive IIA supergravity. Also in this case we derive a dS domain wall interpolating between the Brandhuber-Oz vacuum and the non-supersymmetric AdS$_6$ vacuum of the theory. |
hep-th/0212268 | Daniel Friedan | Daniel Friedan | Two talks on a tentative theory of large distance physics | 21 pages, 4 figures, Latex, Talks given at the Cargese 2002 summer
school | null | null | RUNHETC-2002-51 | hep-th | null | These talks present an overview of a tentative theory of large distance
physics. For each large distance L (in dimensionless units), the theory gives
two complementary descriptions of spacetime physics: quantum field theory at
distances larger than L, string scattering amplitudes at distances smaller than
L. The mechanism of the theory is a certain 2d nonlinear model, the
lambda-model, whose target manifold is the manifold of general nonlinear models
of the worldsurface, the background spacetimes for string scattering. So far,
the theory has only been formulated and its basic working described, in general
terms. The theory's only claims to interest at present are matters of general
principle. It is a self-contained nonperturbative theory of large distance
physics, operating entirely at large distance. The lambda-model constructs an
actual QFT at large distance, a functional integral over spacetime fields. It
constructs an effective background spacetime for string scattering at
relatively small distances. It is background independent, dynamically. Nothing
is adjustable in its formulation. It is a mechanical theory, not an S-matrix
theory. String scattering takes place at small distances within a mechanical
large distance environment. The lambda-model constructs QFT in a way that
offers possibilities of novel physical phenomena at large distances. The task
now is to perform concrete calculations in the lambda-model, to find out if it
produces a physically useful QFT.
| [
{
"created": "Fri, 20 Dec 2002 20:53:04 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Friedan",
"Daniel",
""
]
] | These talks present an overview of a tentative theory of large distance physics. For each large distance L (in dimensionless units), the theory gives two complementary descriptions of spacetime physics: quantum field theory at distances larger than L, string scattering amplitudes at distances smaller than L. The mechanism of the theory is a certain 2d nonlinear model, the lambda-model, whose target manifold is the manifold of general nonlinear models of the worldsurface, the background spacetimes for string scattering. So far, the theory has only been formulated and its basic working described, in general terms. The theory's only claims to interest at present are matters of general principle. It is a self-contained nonperturbative theory of large distance physics, operating entirely at large distance. The lambda-model constructs an actual QFT at large distance, a functional integral over spacetime fields. It constructs an effective background spacetime for string scattering at relatively small distances. It is background independent, dynamically. Nothing is adjustable in its formulation. It is a mechanical theory, not an S-matrix theory. String scattering takes place at small distances within a mechanical large distance environment. The lambda-model constructs QFT in a way that offers possibilities of novel physical phenomena at large distances. The task now is to perform concrete calculations in the lambda-model, to find out if it produces a physically useful QFT. |
hep-th/0703009 | Olaf Lechtenfeld | Johannes Broedel, Tatiana A. Ivanova, Olaf Lechtenfeld | Construction of Noncommutative Instantons in 4k Dimensions | 1+9 pages | Mod.Phys.Lett.A23:179-189,2008 | 10.1142/S0217732308026261 | null | hep-th | null | We consider generalized self-duality equations for U(2r) Yang-Mills theory on
R^{4k} with quaternionic structure and self-dual Moyal deformation. We employ
the extended ADHM method in 4k dimensions to construct new noncommutative
generalizations of the 't Hooft as well as of the BPST instantons. It is shown
that in the commutative limit the BPST-type configurations coincide with the
standard instantons on HP^n written in local coordinates.
| [
{
"created": "Thu, 1 Mar 2007 16:41:07 GMT",
"version": "v1"
}
] | 2008-11-26 | [
[
"Broedel",
"Johannes",
""
],
[
"Ivanova",
"Tatiana A.",
""
],
[
"Lechtenfeld",
"Olaf",
""
]
] | We consider generalized self-duality equations for U(2r) Yang-Mills theory on R^{4k} with quaternionic structure and self-dual Moyal deformation. We employ the extended ADHM method in 4k dimensions to construct new noncommutative generalizations of the 't Hooft as well as of the BPST instantons. It is shown that in the commutative limit the BPST-type configurations coincide with the standard instantons on HP^n written in local coordinates. |
2208.06069 | Andjelo Samsarov | Marija Dimitrijevi\'c \'Ciri\'c, Nikola Konjik, Andjelo Samsarov | Propagation of spinors on a noncommutative spacetime: equivalence of the
formal and the effective approach | 19 pages, no figures; revtex4; references and appendix added, version
to appear in EPJC | Eur. Phys. J. C 83 (2023) 387 | 10.1140/epjc/s10052-023-11540-9 | ZTF-EP-21-07, RBI-ThPhys-2021-41 | hep-th gr-qc | http://creativecommons.org/licenses/by/4.0/ | Some noncommutative (NC) theories posses a certain type of dualities that are
implicitly built within their structure. In this paper we establish still
another example of this kind. More precisely, we show that the noncommutative
U(1) gauge theory coupled to a NC scalar field and to a classical geometry of
the Reissner Nordstrom (RN) type is completely equivalent at the level of
equations of motion to the commutative U(1) gauge theory coupled to a
commutative scalar field and to a classical geometry background, different from
the starting RN background. The new (effective) metric is obtained from the RN
metric by switching on an additional nonvanishing r-phi component. Using this
duality between two theories and physical systems they describe, we formulate
an effective approach to studying a dynamics of spin 1/2 fields on the curved
background of RN type with an abiding noncommutative structure. As opposed to
that, we also study the dynamics of spin 1/2 fields in a more formal way, by
studying the semiclassical theory which describes the NC U(1) gauge field
coupled with NC spin 1/2 field and also with gravity which is however treated
classically. Upon utilising the Seiberg Witten map in order to write the NC
spinor and NC gauge fields in terms of their corresponding commutative degrees
of freedom, we find that the equation of motion for the fermion field obtained
within the formal approach exactly coincides with the equation of motion
obtained within the effective approach that utilises noncommutative duality. We
then use these results to analyze the problem of stability of solutions of the
equations of motion and the associated issue of superradiance, as related to
fermions in RN spacetime with an allpervasive noncommutative structure.
| [
{
"created": "Fri, 12 Aug 2022 00:07:57 GMT",
"version": "v1"
},
{
"created": "Mon, 15 May 2023 20:51:06 GMT",
"version": "v2"
}
] | 2023-05-17 | [
[
"Ćirić",
"Marija Dimitrijević",
""
],
[
"Konjik",
"Nikola",
""
],
[
"Samsarov",
"Andjelo",
""
]
] | Some noncommutative (NC) theories posses a certain type of dualities that are implicitly built within their structure. In this paper we establish still another example of this kind. More precisely, we show that the noncommutative U(1) gauge theory coupled to a NC scalar field and to a classical geometry of the Reissner Nordstrom (RN) type is completely equivalent at the level of equations of motion to the commutative U(1) gauge theory coupled to a commutative scalar field and to a classical geometry background, different from the starting RN background. The new (effective) metric is obtained from the RN metric by switching on an additional nonvanishing r-phi component. Using this duality between two theories and physical systems they describe, we formulate an effective approach to studying a dynamics of spin 1/2 fields on the curved background of RN type with an abiding noncommutative structure. As opposed to that, we also study the dynamics of spin 1/2 fields in a more formal way, by studying the semiclassical theory which describes the NC U(1) gauge field coupled with NC spin 1/2 field and also with gravity which is however treated classically. Upon utilising the Seiberg Witten map in order to write the NC spinor and NC gauge fields in terms of their corresponding commutative degrees of freedom, we find that the equation of motion for the fermion field obtained within the formal approach exactly coincides with the equation of motion obtained within the effective approach that utilises noncommutative duality. We then use these results to analyze the problem of stability of solutions of the equations of motion and the associated issue of superradiance, as related to fermions in RN spacetime with an allpervasive noncommutative structure. |
1401.0261 | Bin Chen | Bin Chen, Feng-yan Song and Jia-ju Zhang | Holographic R\'enyi entropy in AdS$_3$/LCFT$_2$ correspondence | 28 pages. Typos corrected, published version | JHEP 1403 (2014) 137 | 10.1007/JHEP03(2014)137 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The recent study in AdS$_3$/CFT$_2$ correspondence shows that the tree level
contribution and 1-loop correction of holographic R\'enyi entanglement entropy
(HRE) exactly match the direct CFT computation in the large central charge
limit. This allows the R\'enyi entanglement entropy to be a new window to study
the AdS/CFT correspondence. In this paper we generalize the study of R\'enyi
entanglement entropy in pure AdS$_3$ gravity to the massive gravity theories at
the critical points. For the cosmological topological massive gravity (CTMG),
the dual conformal field theory (CFT) could be a chiral conformal field theory
or a logarithmic conformal field theory (LCFT), depending on the asymptotic
boundary conditions imposed. In both cases, by studying the short interval
expansion of the R\'enyi entanglement entropy of two disjoint intervals with
small cross ratio $x$, we find that the classical and 1-loop HRE are in exact
match with the CFT results, up to order $x^6$. To this order, the difference
between the massless graviton and logarithmic mode can be seen clearly.
Moreover, for the cosmological new massive gravity (CNMG) at critical point,
which could be dual to a logarithmic CFT as well, we find the similar agreement
in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of
graviton and logarithmic mode to HRE from CFT computation. It has distinct
feature from the one in pure AdS$_3$ gravity.
| [
{
"created": "Wed, 1 Jan 2014 07:18:51 GMT",
"version": "v1"
},
{
"created": "Sun, 6 Apr 2014 10:25:37 GMT",
"version": "v2"
}
] | 2015-04-29 | [
[
"Chen",
"Bin",
""
],
[
"Song",
"Feng-yan",
""
],
[
"Zhang",
"Jia-ju",
""
]
] | The recent study in AdS$_3$/CFT$_2$ correspondence shows that the tree level contribution and 1-loop correction of holographic R\'enyi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the R\'enyi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of R\'enyi entanglement entropy in pure AdS$_3$ gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the R\'enyi entanglement entropy of two disjoint intervals with small cross ratio $x$, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order $x^6$. To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS$_3$ gravity. |
hep-th/0105205 | David A. Lowe | Gian Luigi Alberghi, Elena Caceres, Kevin Goldstein and David A. Lowe | Stacking non-BPS D-Branes | 10 pages, revtex | Phys.Lett.B520:361-366,2001 | 10.1016/S0370-2693(01)01138-8 | BROWN-HET-1263, IC/2001/27 | hep-th | null | We present a candidate supergravity solution for a stacked configuration of
stable non-BPS D-branes in Type II string theory compactified on T^4/Z_2. This
gives a supergravity description of nonabelian tachyon condensation on the
brane worldvolume.
| [
{
"created": "Mon, 21 May 2001 16:00:30 GMT",
"version": "v1"
},
{
"created": "Wed, 18 Jul 2001 03:12:14 GMT",
"version": "v2"
}
] | 2014-11-18 | [
[
"Alberghi",
"Gian Luigi",
""
],
[
"Caceres",
"Elena",
""
],
[
"Goldstein",
"Kevin",
""
],
[
"Lowe",
"David A.",
""
]
] | We present a candidate supergravity solution for a stacked configuration of stable non-BPS D-branes in Type II string theory compactified on T^4/Z_2. This gives a supergravity description of nonabelian tachyon condensation on the brane worldvolume. |
hep-th/0503220 | Jorge Zanelli | Mokhtar Hassaine, Ricardo Troncoso, and Jorge Zanelli | 11D Supergravity as a gauge theory for the M-algebra | Lecture given at the Fourth International Winter Conference on
Mathematical Methods in Physics, 09 - 13 August 2004, CBPF, Rio de Janeiro,
Brazil. 10 pages, no figures | PoS WC2004 (2005) 006 | null | CECS-PHY-05/06 | hep-th | null | The eleven-dimensional gravitational action invariant under local Poincare
transformations is given by the dimensional continuation of the Euler class of
ten dimensions. Here we show that the supersymmetric extension of this action
leads, through the Noether procedure, to a theory with the local symmetry group
given by the M-algebra. The fields of the theory are the vielbein, the Lorentz
(spin) connection, one gravitino, and two 1-forms which transform as second and
fifth rank antisymmetric Lorentz tensors. These fields are components of a
single connection for the M-algebra and the supersymmetric Lagrangian can be
seen to be a Chern-Simons form. The dynamics has a multiplicity of degenerate
vacua without propagating degrees of freedom. The theory is shown to admit
solutions of the form S^{10-d} x X_{d+1}, where X_{d+1} is a warped product of
R with a d-dimensional spacetime. Among this class, the gravitational effective
action describes a propagating graviton only if d=4 and the spacetime has
positive cosmological constant. The perturbations around this solution
reproduce linearized General Relativity around four-dimensional de Sitter
spacetime.
| [
{
"created": "Mon, 28 Mar 2005 21:13:48 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Hassaine",
"Mokhtar",
""
],
[
"Troncoso",
"Ricardo",
""
],
[
"Zanelli",
"Jorge",
""
]
] | The eleven-dimensional gravitational action invariant under local Poincare transformations is given by the dimensional continuation of the Euler class of ten dimensions. Here we show that the supersymmetric extension of this action leads, through the Noether procedure, to a theory with the local symmetry group given by the M-algebra. The fields of the theory are the vielbein, the Lorentz (spin) connection, one gravitino, and two 1-forms which transform as second and fifth rank antisymmetric Lorentz tensors. These fields are components of a single connection for the M-algebra and the supersymmetric Lagrangian can be seen to be a Chern-Simons form. The dynamics has a multiplicity of degenerate vacua without propagating degrees of freedom. The theory is shown to admit solutions of the form S^{10-d} x X_{d+1}, where X_{d+1} is a warped product of R with a d-dimensional spacetime. Among this class, the gravitational effective action describes a propagating graviton only if d=4 and the spacetime has positive cosmological constant. The perturbations around this solution reproduce linearized General Relativity around four-dimensional de Sitter spacetime. |
hep-th/9703026 | Vladimir Bazhanov | R.M. Ellem, V.V. Bazhanov | Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of
the tricritical Ising model | 22 pages, minor changes, references added. LaTeX file and postscript
figure | Nucl.Phys.B512:563-580,1998 | 10.1016/S0550-3213(97)00748-7 | null | hep-th | null | We give further support to Smirnov's conjecture on the exact kink S-matrix
for the massive Quantum Field Theory describing the integrable perturbation of
the c=0.7 minimal Conformal Field theory (known to describe the tri-critical
Ising model) by the operator $\phi_{2,1}$. This operator has conformal
dimensions $(7/16,7/16)$ and is identified with the subleading magnetic
operator of the tri-critical Ising model. In this paper we apply the
Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by
explicitly utilising its relationship with the solvable lattice hard hexagon
model. Analytically examining the ultraviolet scaling limit we recover the
expected central charge c=0.7 of the tri-critical Ising model. We also compare
numerical values for the ground state energy of the finite size system obtained
from the TBA equations with the results obtained by the Truncated Conformal
Space Approach and Conformal Perturbation Theory.
| [
{
"created": "Tue, 4 Mar 1997 15:15:00 GMT",
"version": "v1"
},
{
"created": "Wed, 5 Mar 1997 01:34:48 GMT",
"version": "v2"
},
{
"created": "Thu, 10 Jul 1997 10:04:21 GMT",
"version": "v3"
}
] | 2011-02-11 | [
[
"Ellem",
"R. M.",
""
],
[
"Bazhanov",
"V. V.",
""
]
] | We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator $\phi_{2,1}$. This operator has conformal dimensions $(7/16,7/16)$ and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory. |
hep-th/9912194 | Vladimir Dzhunushaliev | V. Dzhunushaliev and D. Singleton | Quantization of classical singular solutions in Yang-Mills theory | 18 pgs, REVTEX | Nuovo Cim.B117:137-154,2002 | null | null | hep-th hep-ph | null | In this paper we apply a variant of Heisenberg's quantization method for
strongly interacting, non-linear fields, to solutions of the classical
Yang-Mills field equations which have bad asymptotic behavior. After
quantization we find that the bad features (i.e. divergent fields and energy
densities) of these solutions are moderated. From these results we argue that
in general the n-point Green's functions for Yang-Mills theories can have
non-perturbative pieces which can not be represented as the sum of Feynman
diagrams. A formalism for dealing with these non-Feynman pieces via
nonassociative field operators is suggested. These methods may also find some
application in dealing with high-$T_c$ superconductors.
| [
{
"created": "Tue, 21 Dec 1999 10:04:31 GMT",
"version": "v1"
}
] | 2010-11-11 | [
[
"Dzhunushaliev",
"V.",
""
],
[
"Singleton",
"D.",
""
]
] | In this paper we apply a variant of Heisenberg's quantization method for strongly interacting, non-linear fields, to solutions of the classical Yang-Mills field equations which have bad asymptotic behavior. After quantization we find that the bad features (i.e. divergent fields and energy densities) of these solutions are moderated. From these results we argue that in general the n-point Green's functions for Yang-Mills theories can have non-perturbative pieces which can not be represented as the sum of Feynman diagrams. A formalism for dealing with these non-Feynman pieces via nonassociative field operators is suggested. These methods may also find some application in dealing with high-$T_c$ superconductors. |
hep-th/9606088 | null | L. Faddeev, A. Yu. Volkov | Shift Operator for Nonabelian Lattice Current Algebra | 11 pages, LATEX | Publ.Res.Inst.Math.Sci.Kyoto 40 (2004) 1113-1125 | null | null | hep-th | null | The shift operator for a quantum lattice current algebra associated with
sl(2) is produced in the form of product of local factors. This gives a natural
deformation of the Sugawara construction for discrete space-time.
| [
{
"created": "Fri, 14 Jun 1996 17:44:11 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Faddeev",
"L.",
""
],
[
"Volkov",
"A. Yu.",
""
]
] | The shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time. |
hep-th/0312063 | Klaus Behrndt | Klaus Behrndt and Swapna Mahapatra | De Sitter vacua from N=2 gauged supergravity | 25 pages, 1 figure, add refs and corrected typos | JHEP 0401 (2004) 068 | 10.1088/1126-6708/2004/01/068 | null | hep-th | null | Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle
points of the potential and often the unstable mode runs into a singularity. We
explore the possibility to obtain dS points where the unstable mode goes on
both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity
coupled to the universal hypermultiplet, we have found a potential which has
two supersymmetric minima (one of them can be flat) and these are connected by
a de Sitter saddle point. In order to obtain this potential by an Abelian
gauging, it was important to include the recently proposed quantum corrections
to the universal hypermultiplet sector. Our results apply to four as well as
five dimensional gauged supergravity theories.
| [
{
"created": "Fri, 5 Dec 2003 12:45:32 GMT",
"version": "v1"
},
{
"created": "Fri, 19 Dec 2003 12:34:05 GMT",
"version": "v2"
}
] | 2009-11-10 | [
[
"Behrndt",
"Klaus",
""
],
[
"Mahapatra",
"Swapna",
""
]
] | Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an Abelian gauging, it was important to include the recently proposed quantum corrections to the universal hypermultiplet sector. Our results apply to four as well as five dimensional gauged supergravity theories. |
1006.5714 | Antonio Amariti | A. Amariti, D. Forcella, A. Mariotti, G. Policastro | Holographic Optics and Negative Refractive Index | 20+1 pages, 7 figures | JHEP 1104:036,2011 | 10.1007/JHEP04(2011)036 | null | hep-th cond-mat.other physics.flu-dyn physics.optics | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In recent years a very exciting and intense activity has been devoted to the
understanding and construction of materials that enjoy exotic optical
properties, such as a negative refractive index. Motivated by these
experimental and theoretical developments, we use the string-inspired idea of
holography to study the electromagnetic response of a certain class of media:
strongly coupled relativistic systems that admit a dual gravitational
description. Our results indicate that this type of media generally have a
negative refractive index. Moreover we observe that a negative refractive index
could be a common feature of relativistic hydrodynamic systems at low
frequencies.
| [
{
"created": "Tue, 29 Jun 2010 20:02:33 GMT",
"version": "v1"
}
] | 2011-04-20 | [
[
"Amariti",
"A.",
""
],
[
"Forcella",
"D.",
""
],
[
"Mariotti",
"A.",
""
],
[
"Policastro",
"G.",
""
]
] | In recent years a very exciting and intense activity has been devoted to the understanding and construction of materials that enjoy exotic optical properties, such as a negative refractive index. Motivated by these experimental and theoretical developments, we use the string-inspired idea of holography to study the electromagnetic response of a certain class of media: strongly coupled relativistic systems that admit a dual gravitational description. Our results indicate that this type of media generally have a negative refractive index. Moreover we observe that a negative refractive index could be a common feature of relativistic hydrodynamic systems at low frequencies. |
1610.06693 | Guillaume Bossard | Guillaume Bossard and Boris Pioline | Exact $\nabla^4 R^4$ couplings and helicity supertraces | 40 pages | JHEP 1701 (2017) 050 | 10.1007/JHEP01(2017)050 | CERN-TH-2016-224, CPHT-RR046.102016 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In type II string theory compactified on a $d$-dimensional torus $T^d$ down
to $D=10-d$ dimensions, the $R^4$ and $\nabla^4 R^4$ four-graviton couplings
are known exactly, for all values of the moduli, in terms of certain Eisenstein
series of the U-duality group $E_{d}(\mathbb{Z})$. In the limit where one
circle in the torus becomes large, these couplings are expected to reduce to
their counterpart in dimension $D+1$, plus threshold effects and exponentially
suppressed corrections corresponding to BPS black holes in dimension $D+1$
whose worldline winds around the circle. By combining the weak coupling and
large radius limits, we determine these exponentially suppressed corrections
exactly, and demonstrate that the contributions of 1/4-BPS black holes to the
$\nabla^4 R^4$ coupling are proportional to the appropriate helicity
supertrace. Mathematically, our results provide the complete Fourier expansion
of the next-to-minimal theta series of $E_{d+1}(\mathbb{Z})$ with respect to
the maximal parabolic subgroup with Levi component $E_{d}$ for $d\leq 6$, and
the complete Abelian part of the Fourier expansion of the same for $d=7$.
| [
{
"created": "Fri, 21 Oct 2016 07:46:57 GMT",
"version": "v1"
}
] | 2018-01-22 | [
[
"Bossard",
"Guillaume",
""
],
[
"Pioline",
"Boris",
""
]
] | In type II string theory compactified on a $d$-dimensional torus $T^d$ down to $D=10-d$ dimensions, the $R^4$ and $\nabla^4 R^4$ four-graviton couplings are known exactly, for all values of the moduli, in terms of certain Eisenstein series of the U-duality group $E_{d}(\mathbb{Z})$. In the limit where one circle in the torus becomes large, these couplings are expected to reduce to their counterpart in dimension $D+1$, plus threshold effects and exponentially suppressed corrections corresponding to BPS black holes in dimension $D+1$ whose worldline winds around the circle. By combining the weak coupling and large radius limits, we determine these exponentially suppressed corrections exactly, and demonstrate that the contributions of 1/4-BPS black holes to the $\nabla^4 R^4$ coupling are proportional to the appropriate helicity supertrace. Mathematically, our results provide the complete Fourier expansion of the next-to-minimal theta series of $E_{d+1}(\mathbb{Z})$ with respect to the maximal parabolic subgroup with Levi component $E_{d}$ for $d\leq 6$, and the complete Abelian part of the Fourier expansion of the same for $d=7$. |
2209.11565 | Yuri Markov Adolfovich | Yu.A. Markov, M.A. Markova, A.I. Bondarenko, N.Yu. Markov | Superparticle in an external chiral matter superfield | 24 pages | null | null | null | hep-th | http://creativecommons.org/licenses/by/4.0/ | In this paper the interaction Lagrangian of a superparticle with an external
chiral superfield $\Phi(x,\theta,\bar{\theta})$,invariant with respect to the
global supersymmetry, is proposed. The kinematics of the superparticle is
defined in an extended superspace described by superspace coordinates
$(x_{\mu},\theta_{\alpha},\bar{\theta}_{\alpha})$, where $x_{\mu}$ are pure
bosonic coordinates, $\mu=0,\ldots,3$; $\theta_{\alpha}$ and
$\bar{\theta}_{\alpha}$ are additional fermionic Grassmann-valued spinors. With
the purpose of the construction of the required Lagrangian, chiral analogues of
the supervector $A_{\mu}(x,\theta,\bar{\theta})$ and superspinor
$A_{\alpha}(x,\theta,\bar{\theta})$,
$\bar{A}_{\dot{\alpha}}(x,\theta,\bar{\theta})$ gauge fields are introduced,
which are also matrices in color space. The problem considered in this paper is
the further step in deriving the dynamical equations of motion for a spin
color-charged particle moving in an external fermionic matter field. These
equations of motion are of fundamental importance, for example, when taking
into account the influence of fermionic background fields induced in a hot
quark-gluon plasma (QGP) by thermal fluctuations on the dynamics of hard
color-charged partons crossing the QGP. In turn, the solution of this problem
will make it possible, at least at the qualitative level, to advance in the
study of the motion in the external fermion matter field of such a complex
physical object as a string.
| [
{
"created": "Fri, 23 Sep 2022 12:44:25 GMT",
"version": "v1"
}
] | 2022-09-26 | [
[
"Markov",
"Yu. A.",
""
],
[
"Markova",
"M. A.",
""
],
[
"Bondarenko",
"A. I.",
""
],
[
"Markov",
"N. Yu.",
""
]
] | In this paper the interaction Lagrangian of a superparticle with an external chiral superfield $\Phi(x,\theta,\bar{\theta})$,invariant with respect to the global supersymmetry, is proposed. The kinematics of the superparticle is defined in an extended superspace described by superspace coordinates $(x_{\mu},\theta_{\alpha},\bar{\theta}_{\alpha})$, where $x_{\mu}$ are pure bosonic coordinates, $\mu=0,\ldots,3$; $\theta_{\alpha}$ and $\bar{\theta}_{\alpha}$ are additional fermionic Grassmann-valued spinors. With the purpose of the construction of the required Lagrangian, chiral analogues of the supervector $A_{\mu}(x,\theta,\bar{\theta})$ and superspinor $A_{\alpha}(x,\theta,\bar{\theta})$, $\bar{A}_{\dot{\alpha}}(x,\theta,\bar{\theta})$ gauge fields are introduced, which are also matrices in color space. The problem considered in this paper is the further step in deriving the dynamical equations of motion for a spin color-charged particle moving in an external fermionic matter field. These equations of motion are of fundamental importance, for example, when taking into account the influence of fermionic background fields induced in a hot quark-gluon plasma (QGP) by thermal fluctuations on the dynamics of hard color-charged partons crossing the QGP. In turn, the solution of this problem will make it possible, at least at the qualitative level, to advance in the study of the motion in the external fermion matter field of such a complex physical object as a string. |
2011.09188 | Jerzy Kowalski-Glikman | Michele Arzano, Andrea Bevilacqua, Jerzy Kowalski-Glikman, Giacomo
Rosati, and Josua Unger | $\kappa$-deformed complex fields and discrete symmetries | Coincides with the published version | Phys. Rev. D 103, 106015 (2021) | 10.1103/PhysRevD.103.106015 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We present a construction of $\kappa$-deformed complex scalar field theory
with the objective of shedding light on the way discrete symmetries and CPT
invariance are affected by the deformation. Our starting point is the
observation that, in order to have an appropriate action of Lorentz symmetries
on antiparticle states, these should be described by four-momenta living on the
complement of the portion of de Sitter group manifold to which
$\kappa$-deformed particle four-momenta belong. Once the equations of motions
are properly worked out from the deformed action we obtain that particle and
antiparticle are characterized by different mass-shell constraints leading to a
subtle form of departure from CPT invariance. The remaining part of our work is
dedicated to a detailed description of the action of deformed Poincar\'e and
discrete symmetries on the complex field.
| [
{
"created": "Wed, 18 Nov 2020 10:22:20 GMT",
"version": "v1"
},
{
"created": "Sun, 30 May 2021 07:36:33 GMT",
"version": "v2"
}
] | 2021-06-01 | [
[
"Arzano",
"Michele",
""
],
[
"Bevilacqua",
"Andrea",
""
],
[
"Kowalski-Glikman",
"Jerzy",
""
],
[
"Rosati",
"Giacomo",
""
],
[
"Unger",
"Josua",
""
]
] | We present a construction of $\kappa$-deformed complex scalar field theory with the objective of shedding light on the way discrete symmetries and CPT invariance are affected by the deformation. Our starting point is the observation that, in order to have an appropriate action of Lorentz symmetries on antiparticle states, these should be described by four-momenta living on the complement of the portion of de Sitter group manifold to which $\kappa$-deformed particle four-momenta belong. Once the equations of motions are properly worked out from the deformed action we obtain that particle and antiparticle are characterized by different mass-shell constraints leading to a subtle form of departure from CPT invariance. The remaining part of our work is dedicated to a detailed description of the action of deformed Poincar\'e and discrete symmetries on the complex field. |
hep-th/0405118 | Christopher Herzog | Christopher P. Herzog | Seiberg Duality is an Exceptional Mutation | 32 pages, 4 figures; v2 refs added, "orbifold point" discussion
refined; v3 version to appear in JHEP, discussion of torsion sheaves improved | JHEP0408:064,2004 | 10.1088/1126-6708/2004/08/064 | null | hep-th | null | The low energy gauge theory living on D-branes probing a del Pezzo
singularity of a non-compact Calabi-Yau manifold is not unique. In fact there
is a large equivalence class of such gauge theories related by Seiberg duality.
As a step toward characterizing this class, we show that Seiberg duality can be
defined consistently as an admissible mutation of a strongly exceptional
collection of coherent sheaves.
| [
{
"created": "Thu, 13 May 2004 00:02:06 GMT",
"version": "v1"
},
{
"created": "Mon, 24 May 2004 23:12:38 GMT",
"version": "v2"
},
{
"created": "Thu, 2 Sep 2004 05:51:21 GMT",
"version": "v3"
}
] | 2008-11-26 | [
[
"Herzog",
"Christopher P.",
""
]
] | The low energy gauge theory living on D-branes probing a del Pezzo singularity of a non-compact Calabi-Yau manifold is not unique. In fact there is a large equivalence class of such gauge theories related by Seiberg duality. As a step toward characterizing this class, we show that Seiberg duality can be defined consistently as an admissible mutation of a strongly exceptional collection of coherent sheaves. |
hep-th/9908160 | D'Hoker Eric | E. D'Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis, L. Rastelli | Extremal Correlators in the AdS/CFT Correspondence | 26 pages, LateX, no figures | null | 10.1142/9789812793850_0020 | UCLA/99/TEP/27, MIT-CTP-2893 | hep-th | null | The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr
X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of
the most striking facts to emerge from the AdS/CFT correspondence. A two-fold
puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the
supergravity calculation involves analytic continuation in the k_i variables to
define the product of a vanishing bulk coupling and an infinite integral over
AdS. Second, extremal correlators are uniquely sensitive to mixing of the
single-trace operators $tr X^k$ with protected multi-trace operators in the
same representation of SU(4). We show that the calculation of extremal
correlators from supergravity is subject to the same subtlety of regularization
known for the 2-point functions, and we present a careful method which
justifies the analytic continuation and shows that supergravity fields couple
to single traces without admixture. We also study extremal n-point functions of
chiral primary operators, and argue that Type IIB supergravity requires that
their space-time form is a product of n-1 two-point functions (as in the free
field approximation) multiplied by a non-renormalized coefficient. This
non-renormalization property of extremal n-point functions is a new prediction
of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic
couplings $t \phi \phi$ and $s \phi \phi$ of fields in the dilaton and 5-sphere
graviton towers of Type IIB supergravity on $AdS_5 \times S^5$.
| [
{
"created": "Tue, 24 Aug 1999 23:28:30 GMT",
"version": "v1"
}
] | 2016-11-23 | [
[
"D'Hoker",
"E.",
""
],
[
"Freedman",
"D. Z.",
""
],
[
"Mathur",
"S. D.",
""
],
[
"Matusis",
"A.",
""
],
[
"Rastelli",
"L.",
""
]
] | The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t \phi \phi$ and $s \phi \phi$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 \times S^5$. |
hep-th/0205151 | Annamaria Sinkovics | Nick Dorey and Annamaria Sinkovics | N=1* vacua, Fuzzy Spheres and Integrable Systems | 20 pages | JHEP 0207 (2002) 032 | 10.1088/1126-6708/2002/07/032 | SWAT-339 | hep-th | null | We calculate the exact eigenvalues of the adjoint scalar fields in the
massive vacua of N=1* SUSY Yang-Mills with gauge group SU(N). This provides a
field theory prediction for the distribution of D3 brane charge in the AdS
dual. We verify the proposal of Polchinski and Strassler that the D3-brane's
lie on a fuzzy sphere in the supergravity limit and determine the corrections
to this distribution due to worldsheet and quantum effects. The calculation
also provides several new results concerning the equilibrium configurations of
the N-body Calogero-Moser Hamiltonian.
| [
{
"created": "Wed, 15 May 2002 14:30:12 GMT",
"version": "v1"
}
] | 2009-11-07 | [
[
"Dorey",
"Nick",
""
],
[
"Sinkovics",
"Annamaria",
""
]
] | We calculate the exact eigenvalues of the adjoint scalar fields in the massive vacua of N=1* SUSY Yang-Mills with gauge group SU(N). This provides a field theory prediction for the distribution of D3 brane charge in the AdS dual. We verify the proposal of Polchinski and Strassler that the D3-brane's lie on a fuzzy sphere in the supergravity limit and determine the corrections to this distribution due to worldsheet and quantum effects. The calculation also provides several new results concerning the equilibrium configurations of the N-body Calogero-Moser Hamiltonian. |
1706.04406 | Dionisio Bazeia | D. Bazeia, A. Mohammadi, D.C. Moreira | Fermion bound states in geometrically deformed backgrounds | 8 pages, 12 figures; text and new references added | Chinese Physics C 43 (2019) 013101 | 10.1088/1674-1137/43/1/013101 | null | hep-th cond-mat.mes-hall hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This work deals with the behavior of fermions in the background of kinklike
structures in the two-dimensional spacetime. The kinklike structures appear
from bosonic scalar field models that engender distinct profiles and interact
with the fermion fields via the standard Yukawa coupling. We first consider two
models that engender parity symmetry, one leading to the exclusion of fermion
bound states, and the other to the inclusion of bound states, when the
parameter that controls the bosonic structure varies from zero to unity. We
then go on and investigate another model where the kinklike solution explicitly
breaks parity symmetry, leading to fermion bound states that are spatially
asymmetric.
| [
{
"created": "Wed, 14 Jun 2017 11:08:58 GMT",
"version": "v1"
},
{
"created": "Fri, 16 Jun 2017 17:24:14 GMT",
"version": "v2"
},
{
"created": "Mon, 19 Mar 2018 13:41:42 GMT",
"version": "v3"
}
] | 2019-01-08 | [
[
"Bazeia",
"D.",
""
],
[
"Mohammadi",
"A.",
""
],
[
"Moreira",
"D. C.",
""
]
] | This work deals with the behavior of fermions in the background of kinklike structures in the two-dimensional spacetime. The kinklike structures appear from bosonic scalar field models that engender distinct profiles and interact with the fermion fields via the standard Yukawa coupling. We first consider two models that engender parity symmetry, one leading to the exclusion of fermion bound states, and the other to the inclusion of bound states, when the parameter that controls the bosonic structure varies from zero to unity. We then go on and investigate another model where the kinklike solution explicitly breaks parity symmetry, leading to fermion bound states that are spatially asymmetric. |
1004.4597 | Maxim Konyushikhin | Evgeny Ivanov, Maxim Konyushikhin | N=4, 3D Supersymmetric Quantum Mechanics in Non-Abelian Monopole
Background | 16 pages, reference added, published version | Phys.Rev.D82:085014,2010 | 10.1103/PhysRevD.82.085014 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Using the harmonic superspace approach, we construct the three-dimensional
N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to
an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the
gauge field to be a static form of the 't Hooft ansatz for the 4D self-dual
SU(2) gauge fields, that is a particular solution of Bogomolny equations for
BPS monopoles. We present the explicit form of the corresponding superfield and
component actions, as well as of the quantum Hamiltonian and N=4 supercharges.
The latter can be used to describe a more general N=4 mechanics system, with an
arbitrary BPS monopole background and on-shell N=4 supersymmetry. The essential
feature of our construction is the use of semi-dynamical spin (4,4,0) multiplet
with the Wess-Zumino type action.
| [
{
"created": "Mon, 26 Apr 2010 18:32:41 GMT",
"version": "v1"
},
{
"created": "Fri, 24 Sep 2010 14:53:14 GMT",
"version": "v2"
},
{
"created": "Wed, 15 Dec 2010 15:59:53 GMT",
"version": "v3"
}
] | 2010-12-16 | [
[
"Ivanov",
"Evgeny",
""
],
[
"Konyushikhin",
"Maxim",
""
]
] | Using the harmonic superspace approach, we construct the three-dimensional N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the gauge field to be a static form of the 't Hooft ansatz for the 4D self-dual SU(2) gauge fields, that is a particular solution of Bogomolny equations for BPS monopoles. We present the explicit form of the corresponding superfield and component actions, as well as of the quantum Hamiltonian and N=4 supercharges. The latter can be used to describe a more general N=4 mechanics system, with an arbitrary BPS monopole background and on-shell N=4 supersymmetry. The essential feature of our construction is the use of semi-dynamical spin (4,4,0) multiplet with the Wess-Zumino type action. |
1403.1595 | Daniel Park | Michael R. Douglas, Daniel S. Park and Christian Schnell | The Cremmer-Scherk Mechanism in F-theory Compactifications on K3
Manifolds | 33 pages + appendices, 5 figures; v2: minor corrections, reference
added | null | 10.1007/JHEP05(2014)135 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | It is well understood --- through string dualities --- that there are 20
massless vector fields in the spectrum of eight-dimensional F-theory
compactifications on smooth elliptically fibered K3 surfaces at a generic point
in the K3 moduli space. Such F-theory vacua, which do not have any enhanced
gauge symmetries, can be thought of as supersymmetric type IIB
compactifications on P1 with 24 (p,q) seven-branes. Naively, one might expect
there to be 24 massless vector fields in the eight-dimensional effective theory
coming from world-volume gauge fields of the 24 branes. In this paper, we show
how the vector field spectrum of the eight-dimensional effective theory can be
obtained from the point of view of type IIB supergravity coupled to the
world-volume theory of the seven-branes. In particular, we first show that the
two-forms of the type IIB theory absorb the seven-brane world-volume gauge
fields via the Cremmer-Scherk mechanism. We then proceed to show that the
massless vector fields of the eight-dimensional theory come from KK-reducing
the SL(2,Z) doublet two-forms of type IIB theory along SL(2,Z) doublet
one-forms on the P1. We also discuss the relation between these vector fields
and the "eaten" world-volume vector fields of the seven-branes.
| [
{
"created": "Thu, 6 Mar 2014 21:33:27 GMT",
"version": "v1"
},
{
"created": "Fri, 21 Oct 2016 14:50:56 GMT",
"version": "v2"
}
] | 2016-10-24 | [
[
"Douglas",
"Michael R.",
""
],
[
"Park",
"Daniel S.",
""
],
[
"Schnell",
"Christian",
""
]
] | It is well understood --- through string dualities --- that there are 20 massless vector fields in the spectrum of eight-dimensional F-theory compactifications on smooth elliptically fibered K3 surfaces at a generic point in the K3 moduli space. Such F-theory vacua, which do not have any enhanced gauge symmetries, can be thought of as supersymmetric type IIB compactifications on P1 with 24 (p,q) seven-branes. Naively, one might expect there to be 24 massless vector fields in the eight-dimensional effective theory coming from world-volume gauge fields of the 24 branes. In this paper, we show how the vector field spectrum of the eight-dimensional effective theory can be obtained from the point of view of type IIB supergravity coupled to the world-volume theory of the seven-branes. In particular, we first show that the two-forms of the type IIB theory absorb the seven-brane world-volume gauge fields via the Cremmer-Scherk mechanism. We then proceed to show that the massless vector fields of the eight-dimensional theory come from KK-reducing the SL(2,Z) doublet two-forms of type IIB theory along SL(2,Z) doublet one-forms on the P1. We also discuss the relation between these vector fields and the "eaten" world-volume vector fields of the seven-branes. |
hep-th/0504120 | Juan Francisco Tlapanco | R. Cartas-Fuentevilla and J. F. Tlapanco-Limon | The Kodama state for topological quantum field theory beyond instantons | Introduction and Conclusions have been extended, some appropriate
references have been added. 8 pages. submitted to physics letters B | Phys.Lett. B623 (2005) 165-170 | 10.1016/j.physletb.2005.07.042 | null | hep-th | null | Constructing a symplectic structure that preserves the ordinary symmetries
and the topological invariance for topological Yang-Mills theory, it is shown
that the Kodama (Chern-Simons) state traditionally associated with a
topological phase of unbroken diffeomorphism invariance for instantons, exists
actually for the complete topological sector of the theory. The case of gravity
is briefly discussed.
| [
{
"created": "Wed, 13 Apr 2005 17:58:09 GMT",
"version": "v1"
},
{
"created": "Wed, 22 Jun 2005 22:24:35 GMT",
"version": "v2"
}
] | 2009-11-11 | [
[
"Cartas-Fuentevilla",
"R.",
""
],
[
"Tlapanco-Limon",
"J. F.",
""
]
] | Constructing a symplectic structure that preserves the ordinary symmetries and the topological invariance for topological Yang-Mills theory, it is shown that the Kodama (Chern-Simons) state traditionally associated with a topological phase of unbroken diffeomorphism invariance for instantons, exists actually for the complete topological sector of the theory. The case of gravity is briefly discussed. |
hep-th/0403232 | Raimar Wulkenhaar | Harald Grosse (Vienna), Raimar Wulkenhaar (Leipzig) | Renormalisation of \phi^4-theory on noncommutative R^4 to all orders | 12 pages, 14 figures, LaTeX | Lett. Math. Phys.71:13-26, 2005 | 10.1007/s11005-004-5116-3 | null | hep-th | null | We present the main ideas and techniques of the proof that the
duality-covariant four-dimensional noncommutative \phi^4-model is
renormalisable to all orders. This includes the reformulation as a dynamical
matrix model, the solution of the free theory by orthogonal polynomials as well
as the renormalisation by flow equations involving power-counting theorems for
ribbon graphs drawn on Riemann surfaces.
| [
{
"created": "Tue, 23 Mar 2004 15:48:18 GMT",
"version": "v1"
}
] | 2011-09-16 | [
[
"Grosse",
"Harald",
"",
"Vienna"
],
[
"Wulkenhaar",
"Raimar",
"",
"Leipzig"
]
] | We present the main ideas and techniques of the proof that the duality-covariant four-dimensional noncommutative \phi^4-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the free theory by orthogonal polynomials as well as the renormalisation by flow equations involving power-counting theorems for ribbon graphs drawn on Riemann surfaces. |
hep-th/9307147 | null | H. Aratyn, L.A. Ferreira, J.F. Gomes and A.H. Zimerman | Toda and Volterra Lattice Equations from Discrete Symmetries of KP
Hierarchies | 12 pgs, LaTeX, IFT-P.041/93 | Phys.Lett. B316 (1993) 85-92 | 10.1016/0370-2693(93)90662-2 | null | hep-th nlin.SI solv-int | null | The discrete models of the Toda and Volterra chains are being constructed out
of the continuum two-boson KP hierarchies. The main tool is the discrete
symmetry preserving the Hamiltonian structure of the continuum models. The
two-boson currents of KP hierarchy are being associated with sites of the
corresponding chain by successive actions of discrete symmetry.
| [
{
"created": "Sat, 24 Jul 1993 17:00:51 GMT",
"version": "v1"
}
] | 2009-10-22 | [
[
"Aratyn",
"H.",
""
],
[
"Ferreira",
"L. A.",
""
],
[
"Gomes",
"J. F.",
""
],
[
"Zimerman",
"A. H.",
""
]
] | The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry. |
1211.4887 | Denis Bashkirov | Denis Bashkirov | BLG theories at low values of Chern-Simons coupling | 10 pages, second version, references added | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | It was checked in paper [1] by comparing the moduli spaces and superconformal
indices that two of the BLG theories $(SU(2)_{1}\times SU(2)_{-1})/{\mathbb
Z}_2$ and $SU(2)_2\times SU(2)_{-2}$ are dual to $U(2)_1\times U(2)_{-1}$ and
$U(2)_{2}\times U(2)_{-2}$ ABJM theories, correspondingly. In this paper we
consider the BLG theories $SU(2)_1\times SU(2)_{-1}$ and $(SU(2)_2\times
SU(2)_{-2})/{\mathbb Z}_2$. These theories were noted in [1] to be a tensor
product of two interacting ${\mathcal N}=8$ SCFT's. In this paper we identify
the SCFT's that occur in the product. For both theories one of the sectors is
the IR limit of ${\mathcal N}=8$ SU(2) SYM.
| [
{
"created": "Tue, 20 Nov 2012 21:44:32 GMT",
"version": "v1"
},
{
"created": "Fri, 23 Nov 2012 17:07:25 GMT",
"version": "v2"
}
] | 2012-11-26 | [
[
"Bashkirov",
"Denis",
""
]
] | It was checked in paper [1] by comparing the moduli spaces and superconformal indices that two of the BLG theories $(SU(2)_{1}\times SU(2)_{-1})/{\mathbb Z}_2$ and $SU(2)_2\times SU(2)_{-2}$ are dual to $U(2)_1\times U(2)_{-1}$ and $U(2)_{2}\times U(2)_{-2}$ ABJM theories, correspondingly. In this paper we consider the BLG theories $SU(2)_1\times SU(2)_{-1}$ and $(SU(2)_2\times SU(2)_{-2})/{\mathbb Z}_2$. These theories were noted in [1] to be a tensor product of two interacting ${\mathcal N}=8$ SCFT's. In this paper we identify the SCFT's that occur in the product. For both theories one of the sectors is the IR limit of ${\mathcal N}=8$ SU(2) SYM. |
hep-th/9706189 | Jayme Vaz | Jayme Vaz, Jr. (Syracuse, USA and Campinas, Brazil) | The Dirac Operator over Abelian Finite Groups | 15 pages, LaTeX 2e, amsmath and amssymb packages | null | null | null | hep-th hep-lat | null | In this paper we show how to construct a Dirac operator on a lattice in
complete analogy with the continuum. In fact we consider a more general
problem, that is, the Dirac operator over an abelian finite group (for which a
lattice is a particular example). Our results appear to be in direct connexion
with the so called fermion doubling problem. In order to find this Dirac
operator we need to introduce an algebraic structure (that generalizes the
Clifford algebras) where we have quantities that work as square-root of the
translation operator. Quantities like these square-roots have been used
recently in order to provide an approach to fermions on the lattice that is
free from doubling and has chiral invariance in the massless limit, and our
studies seem to give a mathematical basis to it.
| [
{
"created": "Thu, 26 Jun 1997 13:53:34 GMT",
"version": "v1"
}
] | 2012-08-27 | [
[
"Vaz,",
"Jayme",
"Jr.",
"Syracuse, USA and Campinas, Brazil"
]
] | In this paper we show how to construct a Dirac operator on a lattice in complete analogy with the continuum. In fact we consider a more general problem, that is, the Dirac operator over an abelian finite group (for which a lattice is a particular example). Our results appear to be in direct connexion with the so called fermion doubling problem. In order to find this Dirac operator we need to introduce an algebraic structure (that generalizes the Clifford algebras) where we have quantities that work as square-root of the translation operator. Quantities like these square-roots have been used recently in order to provide an approach to fermions on the lattice that is free from doubling and has chiral invariance in the massless limit, and our studies seem to give a mathematical basis to it. |
2312.00695 | Victor Mishnyakov | A. Mironov, V. Mishnyakov, A. Morozov | Tau-functions beyond the group elements | 16 pages | Nucl. Phys. B1001 (2024) 116504 | 10.1016/j.nuclphysb.2024.116504 | FIAN/TD-15/23, IITP/TH-21/23, ITEP/TH-27/23, MIPT/TH-20/23 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Matrix elements in different representations are connected by quadratic
relations. If matrix elements are those of a $\textit{group element}$, i.e.
satisfying the property $\Delta(X) = X\otimes X$, then their generating
functions obey bilinear Hirota equations and hence are named $\tau$-functions.
However, dealing with group elements is not always easy, especially for
non-commutative algebras of functions, and this slows down the development of
$\tau$-function theory and the study of integrability properties of
non-perturbative functional integrals. A simple way out is to use arbitrary
elements of the universal enveloping algebra, and not just the group elements.
Then the Hirota equations appear to interrelate a whole system of generating
functions, which one may call $\textit{generalized}$ $\tau$-functions. It was
recently demonstrated that this idea can be applicable even to a somewhat
sophisticated case of the quantum toroidal algebra. We consider a number of
simpler examples, including ordinary and quantum groups, to explain how the
method works and what kind of solutions one can obtain.
| [
{
"created": "Fri, 1 Dec 2023 16:28:32 GMT",
"version": "v1"
}
] | 2024-03-11 | [
[
"Mironov",
"A.",
""
],
[
"Mishnyakov",
"V.",
""
],
[
"Morozov",
"A.",
""
]
] | Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $\Delta(X) = X\otimes X$, then their generating functions obey bilinear Hirota equations and hence are named $\tau$-functions. However, dealing with group elements is not always easy, especially for non-commutative algebras of functions, and this slows down the development of $\tau$-function theory and the study of integrability properties of non-perturbative functional integrals. A simple way out is to use arbitrary elements of the universal enveloping algebra, and not just the group elements. Then the Hirota equations appear to interrelate a whole system of generating functions, which one may call $\textit{generalized}$ $\tau$-functions. It was recently demonstrated that this idea can be applicable even to a somewhat sophisticated case of the quantum toroidal algebra. We consider a number of simpler examples, including ordinary and quantum groups, to explain how the method works and what kind of solutions one can obtain. |
1412.8478 | Jaroslav Trnka | Nima Arkani-Hamed, Andrew Hodges, Jaroslav Trnka | Positive Amplitudes In The Amplituhedron | 27 pages, 10 figures | null | 10.1007/JHEP08(2015)030 | CALT-TH-2014-168 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The all-loop integrand for scattering amplitudes in planar N = 4 SYM is
determined by an "amplitude form" with logarithmic singularities on the
boundary of the amplituhedron. In this note we provide strong evidence for a
new striking property of the superamplitude, which we conjecture to be true to
all loop orders: the amplitude form is positive when evaluated inside the
amplituhedron. The statement is sensibly formulated thanks to the natural
"bosonization" of the superamplitude associated with the amplituhedron
geometry. However this positivity is not manifest in any of the current
approaches to scattering amplitudes, and in particular not in the cellulations
of the amplituhedron related to on-shell diagrams and the positive
grassmannian. The surprising positivity of the form suggests the existence of a
"dual amplituhedron" formulation where this feature would be made obvious. We
also suggest that the positivity is associated with an extended picture of
amplituhedron geometry, with the amplituhedron sitting inside a co-dimension
one surface separating "legal" and "illegal" local singularities of the
amplitude. We illustrate this in several simple examples, obtaining new
expressions for amplitudes not associated with any triangulations, but
following in a more invariant manner from a global view of the positive
geometry.
| [
{
"created": "Mon, 29 Dec 2014 21:00:10 GMT",
"version": "v1"
}
] | 2015-09-30 | [
[
"Arkani-Hamed",
"Nima",
""
],
[
"Hodges",
"Andrew",
""
],
[
"Trnka",
"Jaroslav",
""
]
] | The all-loop integrand for scattering amplitudes in planar N = 4 SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a "dual amplituhedron" formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting inside a co-dimension one surface separating "legal" and "illegal" local singularities of the amplitude. We illustrate this in several simple examples, obtaining new expressions for amplitudes not associated with any triangulations, but following in a more invariant manner from a global view of the positive geometry. |
hep-th/9802016 | Rajesh Gopakumar | Rajesh Gopakumar and Cumrun Vafa | Topological Gravity as Large N Topological Gauge Theory | Harvmac, 31 pages (big), references added | Adv.Theor.Math.Phys.2:413-442,1998 | null | HUTP-97/A105, UCSB-97-25 | hep-th | null | We consider topological closed string theories on Calabi-Yau manifolds which
compute superpotential terms in the corresponding compactified type II
effective action. In particular, near certain singularities we compare the
partition function of this topological theory (the Kodaira-Spencer theory) to
$SU(\infty)$ Chern-Simons theory on the vanishing 3-cycle. We find agreement
between these theories, which we check explicitly for the case of shrinking
$S^3$ and Lens spaces, at the perturbative level. Moreover, the gauge theory
has non-perturbative contributions which have a natural interpretation in the
Type IIB picture. We provide a heuristic explanation for this agreement as well
as suggest further equivalences in other topological gravity/gauge systems.
| [
{
"created": "Tue, 3 Feb 1998 20:29:17 GMT",
"version": "v1"
},
{
"created": "Wed, 18 Feb 1998 21:54:22 GMT",
"version": "v2"
}
] | 2008-11-26 | [
[
"Gopakumar",
"Rajesh",
""
],
[
"Vafa",
"Cumrun",
""
]
] | We consider topological closed string theories on Calabi-Yau manifolds which compute superpotential terms in the corresponding compactified type II effective action. In particular, near certain singularities we compare the partition function of this topological theory (the Kodaira-Spencer theory) to $SU(\infty)$ Chern-Simons theory on the vanishing 3-cycle. We find agreement between these theories, which we check explicitly for the case of shrinking $S^3$ and Lens spaces, at the perturbative level. Moreover, the gauge theory has non-perturbative contributions which have a natural interpretation in the Type IIB picture. We provide a heuristic explanation for this agreement as well as suggest further equivalences in other topological gravity/gauge systems. |
1104.5366 | Astrid Eichhorn | Astrid Eichhorn and Holger Gies | Light fermions in quantum gravity | 16 pages, 9 figures | null | 10.1088/1367-2630/13/12/125012 | null | hep-th gr-qc hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the impact of quantum gravity, formulated as a quantum field theory
of the metric, on chiral symmetry in a fermionic matter sector. We specifically
address the question as to whether metric fluctuations can induce chiral
symmetry breaking and bound state formation. Our results based on the
functional Renormalization Group indicate that chiral symmetry is left intact
even at strong gravitational coupling. In particular, we find that
asymptotically safe quantum gravity where the gravitational couplings approach
a non-Gaussian fixed point generically admits universes with light fermions.
Our results thus further support quantum gravity theories built on fluctuations
of the metric field such as the asymptotic-safety scenario. A study of chiral
symmetry breaking through gravitational quantum effects may serve as a
significant benchmark test also for other quantum gravity scenarios, since a
completely broken chiral symmetry at the Planck scale would not be in
accordance with the observation of light fermions in our universe. We
demonstrate that this elementary observation already imposes constraints on a
generic UV completion of gravity.
| [
{
"created": "Thu, 28 Apr 2011 12:11:08 GMT",
"version": "v1"
}
] | 2015-05-28 | [
[
"Eichhorn",
"Astrid",
""
],
[
"Gies",
"Holger",
""
]
] | We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. We specifically address the question as to whether metric fluctuations can induce chiral symmetry breaking and bound state formation. Our results based on the functional Renormalization Group indicate that chiral symmetry is left intact even at strong gravitational coupling. In particular, we find that asymptotically safe quantum gravity where the gravitational couplings approach a non-Gaussian fixed point generically admits universes with light fermions. Our results thus further support quantum gravity theories built on fluctuations of the metric field such as the asymptotic-safety scenario. A study of chiral symmetry breaking through gravitational quantum effects may serve as a significant benchmark test also for other quantum gravity scenarios, since a completely broken chiral symmetry at the Planck scale would not be in accordance with the observation of light fermions in our universe. We demonstrate that this elementary observation already imposes constraints on a generic UV completion of gravity. |
2109.02725 | Charlotte Sleight | Charlotte Sleight and Massimo Taronna | From dS to AdS and back | 82 pages, 19 figures. v2: typos fixed | null | 10.1007/JHEP12(2021)074 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We describe in more detail the general relation uncovered in our previous
work between boundary correlators in de Sitter (dS) and in Euclidean anti-de
Sitter (EAdS) space, at any order in perturbation theory. Assuming the
Bunch-Davies vacuum at early times, any given diagram contributing to a
boundary correlator in dS can be expressed as a linear combination of Witten
diagrams for the corresponding process in EAdS, where the relative coefficients
are fixed by consistent on-shell factorisation in dS. These coefficients are
given by certain sinusoidal factors which account for the change in coefficient
of the contact sub-diagrams from EAdS to dS, which we argue encode
(perturbative) unitary time evolution in dS. dS boundary correlators with
Bunch-Davies initial conditions thus perturbatively have the same singularity
structure as their Euclidean AdS counterparts and the identities between them
allow to directly import the wealth of techniques, results and understanding
from AdS to dS. This includes the Conformal Partial Wave expansion and, by
going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the
Froissart-Gribov inversion formula. We give a few (among the many possible)
applications both at tree and loop level. Such identities between boundary
correlators in dS and EAdS are made manifest by the Mellin-Barnes
representation of boundary correlators, which we point out is a useful tool in
its own right as the analogue of the Fourier transform for the dilatation
group. The Mellin-Barnes representation in particular makes manifest
factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS,
which imply Cutkosky cutting rules and dispersion formulas for boundary
correlators in (EA)dS. Our results are completely general and in particular
apply to any interaction of (integer) spinning fields.
| [
{
"created": "Mon, 6 Sep 2021 20:28:23 GMT",
"version": "v1"
},
{
"created": "Mon, 13 Sep 2021 07:57:08 GMT",
"version": "v2"
}
] | 2022-01-05 | [
[
"Sleight",
"Charlotte",
""
],
[
"Taronna",
"Massimo",
""
]
] | We describe in more detail the general relation uncovered in our previous work between boundary correlators in de Sitter (dS) and in Euclidean anti-de Sitter (EAdS) space, at any order in perturbation theory. Assuming the Bunch-Davies vacuum at early times, any given diagram contributing to a boundary correlator in dS can be expressed as a linear combination of Witten diagrams for the corresponding process in EAdS, where the relative coefficients are fixed by consistent on-shell factorisation in dS. These coefficients are given by certain sinusoidal factors which account for the change in coefficient of the contact sub-diagrams from EAdS to dS, which we argue encode (perturbative) unitary time evolution in dS. dS boundary correlators with Bunch-Davies initial conditions thus perturbatively have the same singularity structure as their Euclidean AdS counterparts and the identities between them allow to directly import the wealth of techniques, results and understanding from AdS to dS. This includes the Conformal Partial Wave expansion and, by going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the Froissart-Gribov inversion formula. We give a few (among the many possible) applications both at tree and loop level. Such identities between boundary correlators in dS and EAdS are made manifest by the Mellin-Barnes representation of boundary correlators, which we point out is a useful tool in its own right as the analogue of the Fourier transform for the dilatation group. The Mellin-Barnes representation in particular makes manifest factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS, which imply Cutkosky cutting rules and dispersion formulas for boundary correlators in (EA)dS. Our results are completely general and in particular apply to any interaction of (integer) spinning fields. |
hep-th/0408079 | Davide Fioravanti | Davide Fioravanti | Geometrical Loci and CFTs via the Virasoro Symmetry of the mKdV-SG
hierarchy: an excursus | LaTex, 9 pages | Phys.Lett. B609 (2005) 173-179 | 10.1016/j.physletb.2005.01.037 | APCTP 2004-001 | hep-th math-ph math.MP nlin.SI | null | We will describe the appearance of specific algebraic KdV potentials as a
consequence of a requirement on a integro-differential expression. This
expression belongs to a class generated by means of Virasoro vector fields
acting on the KdV field. The ``almost'' rational KdV fields are described in
terms of a geometrical locus of complex points. A class of solutions of this
locus has recently appeared as a description of any conformal Verma module
without degeneration.
| [
{
"created": "Tue, 10 Aug 2004 16:23:18 GMT",
"version": "v1"
}
] | 2010-04-05 | [
[
"Fioravanti",
"Davide",
""
]
] | We will describe the appearance of specific algebraic KdV potentials as a consequence of a requirement on a integro-differential expression. This expression belongs to a class generated by means of Virasoro vector fields acting on the KdV field. The ``almost'' rational KdV fields are described in terms of a geometrical locus of complex points. A class of solutions of this locus has recently appeared as a description of any conformal Verma module without degeneration. |
1510.01252 | Alexei Morozov | Ya.Kononov and A.Morozov | Colored HOMFLY and Generalized Mandelbrot set | 16 pages | JHEP 1511 (2015) 151 | 10.1007/JHEP11(2015)151 | IITP/TH-11/15 | hep-th math-ph math.GT math.MP nlin.CD | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Mandelbrot set is a closure of the set of zeroes of $resultant_x(F_n,F_m)$
for iterated maps $F_n(x)=f^{\circ n}(x)-x$ in the moduli space of maps $f(x)$.
The wonderful fact is that for a given $n$ all zeroes are not chaotically
scattered around the moduli space, but lie on smooth curves, with just a few
cusps, located at zeroes of $discriminant_x(F_n)$. We call this phenomenon the
Mandelbrot property. If approached by the cabling method, symmetrically-colored
HOMFLY polynomials $H^{\cal K}_n(A|q)$ can be considered as linear forms on the
$n$-th "power" of the knot ${\cal K}$, and one can wonder if zeroes of
$resultant_{q^2}(H_n,H_m)$ can also possess the Mandelbrot property. We present
and discuss such resultant-zeroes patterns in the complex-$A$ plane. Though $A$
is hardly an adequate parameter to describe the moduli space of knots, the
Mandelbrot-like structure is clearly seen -- in full accord with the vision of
arXiv:hep-th/0501235, that concrete slicing of the Universal Mandelbrot set is
not essential for revealing its structure.
| [
{
"created": "Mon, 5 Oct 2015 17:30:24 GMT",
"version": "v1"
}
] | 2017-05-02 | [
[
"Kononov",
"Ya.",
""
],
[
"Morozov",
"A.",
""
]
] | Mandelbrot set is a closure of the set of zeroes of $resultant_x(F_n,F_m)$ for iterated maps $F_n(x)=f^{\circ n}(x)-x$ in the moduli space of maps $f(x)$. The wonderful fact is that for a given $n$ all zeroes are not chaotically scattered around the moduli space, but lie on smooth curves, with just a few cusps, located at zeroes of $discriminant_x(F_n)$. We call this phenomenon the Mandelbrot property. If approached by the cabling method, symmetrically-colored HOMFLY polynomials $H^{\cal K}_n(A|q)$ can be considered as linear forms on the $n$-th "power" of the knot ${\cal K}$, and one can wonder if zeroes of $resultant_{q^2}(H_n,H_m)$ can also possess the Mandelbrot property. We present and discuss such resultant-zeroes patterns in the complex-$A$ plane. Though $A$ is hardly an adequate parameter to describe the moduli space of knots, the Mandelbrot-like structure is clearly seen -- in full accord with the vision of arXiv:hep-th/0501235, that concrete slicing of the Universal Mandelbrot set is not essential for revealing its structure. |
hep-th/0401237 | Michael Wohlgenannt | Stefan Denk, Volkmar Putz, Manfred Schweda and Michael Wohlgenannt | Towards UV Finite Quantum Field Theories from Non-Local Field Operators | 22 pages, 4 figures | Eur.Phys.J. C35 (2004) 283-292 | 10.1140/epjc/s2004-01783-7 | TUW-04-03 | hep-th | null | A non-local toy model whose interaction consists of smeared, non-local field
operators is presented. We work out the Feynman rules and propose a power
counting formula for arbitrary graphs. Explicit calculations for one loop
graphs show that their contribution is finite for sufficient smearing and agree
with the power counting formula. UV/IR mixing does not occur.
| [
{
"created": "Fri, 30 Jan 2004 11:33:48 GMT",
"version": "v1"
}
] | 2009-11-10 | [
[
"Denk",
"Stefan",
""
],
[
"Putz",
"Volkmar",
""
],
[
"Schweda",
"Manfred",
""
],
[
"Wohlgenannt",
"Michael",
""
]
] | A non-local toy model whose interaction consists of smeared, non-local field operators is presented. We work out the Feynman rules and propose a power counting formula for arbitrary graphs. Explicit calculations for one loop graphs show that their contribution is finite for sufficient smearing and agree with the power counting formula. UV/IR mixing does not occur. |
1312.1108 | Roberto Emparan | Roberto Emparan, Kentaro Tanabe | Holographic superconductivity in the large D expansion | 21 pages, 7 figures. v2: minor clarifications, refs added, lighter
pdf file | JHEP 01 (2014) 145 | 10.1007/JHEP01(2014)145 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study holographic superconductivity by expanding the equations in the
inverse of the number of spacetime dimensions D. We obtain an analytic
expression for the critical temperature as a function of the conformal
dimension of the condensate operator. Its accuracy for 3+1-dimensional
superconductors is better than 15%. The analysis reveals a simple, and
quantitative, explanation for the onset of the superconducting instability, as
well as universal features of holographic superconductivity in the large D
limit. In particular, this allows to easily compute the effects of backreaction
on the critical temperature.
| [
{
"created": "Wed, 4 Dec 2013 11:07:53 GMT",
"version": "v1"
},
{
"created": "Tue, 10 Dec 2013 15:44:20 GMT",
"version": "v2"
}
] | 2022-03-07 | [
[
"Emparan",
"Roberto",
""
],
[
"Tanabe",
"Kentaro",
""
]
] | We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the condensate operator. Its accuracy for 3+1-dimensional superconductors is better than 15%. The analysis reveals a simple, and quantitative, explanation for the onset of the superconducting instability, as well as universal features of holographic superconductivity in the large D limit. In particular, this allows to easily compute the effects of backreaction on the critical temperature. |
hep-th/0110268 | Chen-Gang Zhou | Chengang Zhou | Deformation Quantization and Quantum Field Theory on Curved Spaces: the
Case of Two-Sphere | 23 pages | null | null | RUNHETC-2001-31 | hep-th | null | We study the scalar quantum field theory on a generic noncommutative
two-sphere as a special case of noncommutative curved space, which is described
by the deformation quantization algebra obtained from symplectic reduction and
parametrized by $H^2(S^2, \QR)$. The fuzzy sphere is included as a special case
parametrized by the integer two-cohomology class $H^2(S^2, \QZ)$, which has
finite number of degrees of freedom and the field theory has a well defined
Hilbert space. When the two-cohomology class is not integer valued, the scalar
quantum field theory based on the deformation algebra is not unitary: the
signature of the inner product on the space of functions is indefinite. Hence
the existence of deformation quantization does not guarantee a physically
acceptable deformed geometric background. For the deformation quantization on a
general curved space, this obstruction of unitarity can be given by an explicit
topological formula.
| [
{
"created": "Mon, 29 Oct 2001 21:11:10 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Zhou",
"Chengang",
""
]
] | We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized by $H^2(S^2, \QR)$. The fuzzy sphere is included as a special case parametrized by the integer two-cohomology class $H^2(S^2, \QZ)$, which has finite number of degrees of freedom and the field theory has a well defined Hilbert space. When the two-cohomology class is not integer valued, the scalar quantum field theory based on the deformation algebra is not unitary: the signature of the inner product on the space of functions is indefinite. Hence the existence of deformation quantization does not guarantee a physically acceptable deformed geometric background. For the deformation quantization on a general curved space, this obstruction of unitarity can be given by an explicit topological formula. |
hep-th/0501248 | Takao Koikawa | Takao Koikawa | Infinite number of soliton solutions to 5-dimensional vacuum Einstein
equation | 13 pages | Prog.Theor.Phys. 114 (2005) 793-803 | 10.1143/PTP.114.793 | null | hep-th | null | We give an infinite number of exact solutions to the 5-dimensional static
Einstein equation with axial symmetry by using the inverse scattering method.
The solutions are characterized by two integers representing the soliton
numbers. The first non trivial example of these solutions is the static black
ring solution found recently.
| [
{
"created": "Sun, 30 Jan 2005 20:24:36 GMT",
"version": "v1"
}
] | 2009-11-11 | [
[
"Koikawa",
"Takao",
""
]
] | We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The first non trivial example of these solutions is the static black ring solution found recently. |
1311.1276 | Matthew Buican | Matthew Buican | Minimal Distances Between SCFTs | 41 pages and 2 figures; references updated; minor improvements in
examples section | null | 10.1007/JHEP01(2014)155 | null | hep-th hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study lower bounds on the minimal distance in theory space between
four-dimensional superconformal field theories (SCFTs) connected via broad
classes of renormalization group (RG) flows preserving various amounts of
supersymmetry (SUSY). For N=1 RG flows, the ultraviolet (UV) and infrared (IR)
endpoints of the flow can be parametrically close. On the other hand, for RG
flows emanating from a maximally supersymmetric SCFT, the distance to the IR
theory cannot be arbitrarily small regardless of the amount of (non-trivial)
SUSY preserved along the flow. The case of RG flows from N=2 UV SCFTs is more
subtle. We argue that for RG flows preserving the full N=2 SUSY, there are
various obstructions to finding examples with parametrically close UV and IR
endpoints. Under reasonable assumptions, these obstructions include: unitarity,
known bounds on the c central charge derived from associativity of the operator
product expansion, and the central charge bounds of Hofman and Maldacena. On
the other hand, for RG flows that break N=2 to N=1, it is possible to find IR
fixed points that are parametrically close to the UV ones. In this case, we
argue that if the UV SCFT possesses a single stress tensor, then such RG flows
excite of order all the degrees of freedom of the UV theory. Furthermore, if
the UV theory has some flavor symmetry, we argue that the UV central charges
should not be too large relative to certain parameters in the theory.
| [
{
"created": "Wed, 6 Nov 2013 02:59:46 GMT",
"version": "v1"
},
{
"created": "Mon, 18 Nov 2013 00:09:59 GMT",
"version": "v2"
}
] | 2015-06-17 | [
[
"Buican",
"Matthew",
""
]
] | We study lower bounds on the minimal distance in theory space between four-dimensional superconformal field theories (SCFTs) connected via broad classes of renormalization group (RG) flows preserving various amounts of supersymmetry (SUSY). For N=1 RG flows, the ultraviolet (UV) and infrared (IR) endpoints of the flow can be parametrically close. On the other hand, for RG flows emanating from a maximally supersymmetric SCFT, the distance to the IR theory cannot be arbitrarily small regardless of the amount of (non-trivial) SUSY preserved along the flow. The case of RG flows from N=2 UV SCFTs is more subtle. We argue that for RG flows preserving the full N=2 SUSY, there are various obstructions to finding examples with parametrically close UV and IR endpoints. Under reasonable assumptions, these obstructions include: unitarity, known bounds on the c central charge derived from associativity of the operator product expansion, and the central charge bounds of Hofman and Maldacena. On the other hand, for RG flows that break N=2 to N=1, it is possible to find IR fixed points that are parametrically close to the UV ones. In this case, we argue that if the UV SCFT possesses a single stress tensor, then such RG flows excite of order all the degrees of freedom of the UV theory. Furthermore, if the UV theory has some flavor symmetry, we argue that the UV central charges should not be too large relative to certain parameters in the theory. |
1911.08921 | Sebasti\'an Alberto Franchino Vi\~nas | Sebasti\'an A. Franchino-Vi\~nas, Salvatore Mignemi | Asymptotic freedom for $\lambda \phi^4_{\star}$ QFT in Snyder-de Sitter
space | 14 pages, 3 figures. v2: corrects factors 2 in eq. (7) and (8), and
eq. (19) regarding the discussion of $m_{\rm eff}$ and $\alpha_{\rm eff}$ | null | 10.1140/epjc/s10052-020-7918-6 | null | hep-th gr-qc math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We analyze the model of a self-interacting $\phi^4_{\star}$ scalar field
theory in Snyder-de Sitter space. After analytically computing the one-loop
beta functions {in the small noncommutativity and curvature limit}, we solve
numerically the corresponding system of differential equations, showing that in
this limit the model possesses at least one regime in which the theory is
asymptotically free. Moreover, in a given region of the parameter space we also
observe a peculiar running of the parameter associated to the curvature, which
changes its sign and therefore can be interpreted as a transition from an IR
de-Sitter space to and UV anti-de Sitter one.
| [
{
"created": "Wed, 20 Nov 2019 14:07:21 GMT",
"version": "v1"
},
{
"created": "Wed, 31 Mar 2021 10:51:20 GMT",
"version": "v2"
}
] | 2021-04-01 | [
[
"Franchino-Viñas",
"Sebastián A.",
""
],
[
"Mignemi",
"Salvatore",
""
]
] | We analyze the model of a self-interacting $\phi^4_{\star}$ scalar field theory in Snyder-de Sitter space. After analytically computing the one-loop beta functions {in the small noncommutativity and curvature limit}, we solve numerically the corresponding system of differential equations, showing that in this limit the model possesses at least one regime in which the theory is asymptotically free. Moreover, in a given region of the parameter space we also observe a peculiar running of the parameter associated to the curvature, which changes its sign and therefore can be interpreted as a transition from an IR de-Sitter space to and UV anti-de Sitter one. |
1309.1087 | Leopoldo A. Pando Zayas | Benjamin Burrington, Leopoldo A. Pando Zayas and Nicholas Rombes | On Resolutions of Cosmological Singularities in Higher-Spin Gravity | 24 pages. v2: typos fixed, references added | null | null | MCTP-13-25 | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the resolution of certain cosmological singularity in the context of
higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3
field realized as Chern-Simons theory with gauge group $SL(3,\mathbb{C})$. In
this context we elaborate and extend a singularity resolution scheme proposed
by Krishnan and Roy. We discuss the resolution of a big-bang singularity in the
case of gravity coupled to a spin-4 field realized as Chern-Simons theory with
gauge group $SL(4,\mathbb{C})$. In all these cases we show the existence of
gauge transformations that do not change the holonomy of the Chern-Simons gauge
potential and lead to metrics without the initial singularity. We argue that
such transformations always exist in the context of gravity coupled to a spin-N
field when described by Chern-Simons with gauge group $SL(N,\mathbb{C})$.
| [
{
"created": "Wed, 4 Sep 2013 16:16:13 GMT",
"version": "v1"
},
{
"created": "Mon, 9 Sep 2013 14:13:46 GMT",
"version": "v2"
}
] | 2013-09-10 | [
[
"Burrington",
"Benjamin",
""
],
[
"Zayas",
"Leopoldo A. Pando",
""
],
[
"Rombes",
"Nicholas",
""
]
] | We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern-Simons theory with gauge group $SL(3,\mathbb{C})$. In this context we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big-bang singularity in the case of gravity coupled to a spin-4 field realized as Chern-Simons theory with gauge group $SL(4,\mathbb{C})$. In all these cases we show the existence of gauge transformations that do not change the holonomy of the Chern-Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-N field when described by Chern-Simons with gauge group $SL(N,\mathbb{C})$. |
1101.4009 | Christopher Pope | S. Deser, Haishan Liu, H. Lu, C.N. Pope, Tahsin Cagri Sisman, Bayram
Tekin | Critical Points of D-Dimensional Extended Gravities | 6 pages, typos corrected | Phys.Rev.D83:061502,2011 | 10.1103/PhysRevD.83.061502 | BRX-TH-632, CALT 68-281, MIFPA-11-04 | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the parameter space of D-dimensional cosmological Einstein gravity
together with quadratic curvature terms. In D>4 there are in general two
distinct (anti)-de Sitter vacua. We show that for appropriate choice of the
parameters there exists a critical point for one of the vacua, for which there
are only massless tensor, but neither massive tensor nor scalar, gravitons. At
criticality, the linearized excitations have vanishing energy (as do black hole
solutions). A further restriction of the parameters gives a one-parameter
cosmological Einstein plus Weyl^2 model with a unique vacuum, whose \Lambda is
determined.
| [
{
"created": "Thu, 20 Jan 2011 20:32:16 GMT",
"version": "v1"
},
{
"created": "Sun, 30 Jan 2011 20:49:22 GMT",
"version": "v2"
}
] | 2011-03-22 | [
[
"Deser",
"S.",
""
],
[
"Liu",
"Haishan",
""
],
[
"Lu",
"H.",
""
],
[
"Pope",
"C. N.",
""
],
[
"Sisman",
"Tahsin Cagri",
""
],
[
"Tekin",
"Bayram",
""
]
] | We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, whose \Lambda is determined. |
0903.2859 | Francesco Nitti | U. Gursoy, E. Kiritsis, L. Mazzanti, F. Nitti | Improved Holographic Yang-Mills at Finite Temperature: Comparison with
Data | 36 pages, 10 figures; references added, minor typos corrected; v3:
corrected numerical mistake in section 5.4. | Nucl.Phys.B820:148-177,2009 | 10.1016/j.nuclphysb.2009.05.017 | null | hep-th hep-lat hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The semi-phenomenological improved holographic model for QCD is confronted
with data of the pure glue, large-Nc gauge theory. After fitting two
phenomenological parameters in the potential, the model can reproduce in detail
all thermodynamic functions at finite temperature. It also reproduces in detail
all known spin-0 and spin-2 glueball observables at zero temperature and
predicts the rest of the 0++ and 2++ towers. A similar two parameter fit in the
CP-odd sector postdicts the correct second 0+- glueball mass, and predicts the
rest of the 0+- tower.
| [
{
"created": "Mon, 16 Mar 2009 21:11:24 GMT",
"version": "v1"
},
{
"created": "Fri, 3 Jul 2009 16:52:12 GMT",
"version": "v2"
},
{
"created": "Fri, 30 Apr 2010 11:29:03 GMT",
"version": "v3"
}
] | 2010-05-07 | [
[
"Gursoy",
"U.",
""
],
[
"Kiritsis",
"E.",
""
],
[
"Mazzanti",
"L.",
""
],
[
"Nitti",
"F.",
""
]
] | The semi-phenomenological improved holographic model for QCD is confronted with data of the pure glue, large-Nc gauge theory. After fitting two phenomenological parameters in the potential, the model can reproduce in detail all thermodynamic functions at finite temperature. It also reproduces in detail all known spin-0 and spin-2 glueball observables at zero temperature and predicts the rest of the 0++ and 2++ towers. A similar two parameter fit in the CP-odd sector postdicts the correct second 0+- glueball mass, and predicts the rest of the 0+- tower. |
hep-th/9302010 | null | T. Brzezinski, J. Rembielinski, K.A. Smolinski | Quantum Particle on a Quantum Circle | 11 pages, LaTeX | Mod.Phys.Lett.A8:409-416,1993 | 10.1142/S0217732393000416 | KFT UL 10/92 | hep-th | null | We describe a $q$-deformed dynamical system corresponding to the quantum free
particle moving along the circle. The algebra of observables is constructed and
discussed. We construct and classify irreducible representations of the system.
| [
{
"created": "Wed, 3 Feb 1993 09:20:26 GMT",
"version": "v1"
},
{
"created": "Fri, 12 Feb 1993 09:50:30 GMT",
"version": "v2"
}
] | 2010-11-01 | [
[
"Brzezinski",
"T.",
""
],
[
"Rembielinski",
"J.",
""
],
[
"Smolinski",
"K. A.",
""
]
] | We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system. |
1201.3098 | Cristian Stelea | Yves Brihaye, Eugen Radu, and Cristian Stelea | Charged squashed black holes with negative cosmological constant in odd
dimensions | 11 pages, 3 figures, v2 added references | null | 10.1016/j.physletb.2012.02.035 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We construct new electrically charged solutions of the Einstein-Maxwell
equations with negative cosmological constant in general odd dimensions $d=2n+3
\geq 5$. They correspond to higher dimensional generalizations of the squashed
black hole solutions, which were known so far only in five dimensions. We
explore numerically the general properties of such classical solutions and,
using a counterterm prescription, we compute their conserved charges and
discuss their thermodynamics.
| [
{
"created": "Sun, 15 Jan 2012 15:57:34 GMT",
"version": "v1"
},
{
"created": "Wed, 25 Jan 2012 11:32:01 GMT",
"version": "v2"
}
] | 2015-06-03 | [
[
"Brihaye",
"Yves",
""
],
[
"Radu",
"Eugen",
""
],
[
"Stelea",
"Cristian",
""
]
] | We construct new electrically charged solutions of the Einstein-Maxwell equations with negative cosmological constant in general odd dimensions $d=2n+3 \geq 5$. They correspond to higher dimensional generalizations of the squashed black hole solutions, which were known so far only in five dimensions. We explore numerically the general properties of such classical solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. |
hep-th/9903062 | Hiroaki Terashima | Hiroaki Terashima (Univ. of Tokyo) | Fluctuation-dissipation theorem and the Unruh effect of scalar and Dirac
fields | 26 pages | Phys. Rev. D 60, 084001 (1999) | 10.1103/PhysRevD.60.084001 | UT-839 | hep-th gr-qc | null | We present a simple and systematic method to calculate the Rindler noise,
which is relevant to the analysis of the Unruh effect, by using the
fluctuation-dissipative theorem. To do this, we calculate the dissipative
coefficient explicitly from the equations of motion of the detector and the
field. This method gives not only the correct answer but also a hint as to the
origin of the apparent statistics inversion effect. Moreover, this method is
generalized to the Dirac field, by using the fermionic fluctuation-dissipation
theorem. We can thus confirm that the fermionic fluctuation-dissipation theorem
is working properly.
| [
{
"created": "Mon, 8 Mar 1999 08:31:48 GMT",
"version": "v1"
}
] | 2016-08-25 | [
[
"Terashima",
"Hiroaki",
"",
"Univ. of Tokyo"
]
] | We present a simple and systematic method to calculate the Rindler noise, which is relevant to the analysis of the Unruh effect, by using the fluctuation-dissipative theorem. To do this, we calculate the dissipative coefficient explicitly from the equations of motion of the detector and the field. This method gives not only the correct answer but also a hint as to the origin of the apparent statistics inversion effect. Moreover, this method is generalized to the Dirac field, by using the fermionic fluctuation-dissipation theorem. We can thus confirm that the fermionic fluctuation-dissipation theorem is working properly. |
hep-th/9712234 | Chie Ohzeki | T. Miyazaki, C. Ohzeki and M. Yamanobe | $(p+2)$-form gauge fields for $p$-brane through an action-at-a-distance | 6 pages | Nuovo Cim. B114 (1999) 589-593 | null | null | hep-th | null | In the conventional $p$-brane theory, a gauge ($p+1$)-form field
$\phi^{(p+1)}$ mediates the interaction between $p$-branes, which is gauge
invariant in the sense $\phi^{(p+1)}\to \phi^{(p+1)}+d\Lambda^{(p)}$ with
$\Lambda^{(p)}$, an arbitrary $p$-form and $d$, a boundary operator. We, on the
contrary, propose to introduce a new gauge field $\phi^{(p+2)}$ mediating the
interaction, and we have a new type of gauge transformation: $\phi^{(p+2)}\to
\phi^{(p+2)} +\delta\Lambda^{(p+3)}$, with $\delta$, a coboundary operator.
| [
{
"created": "Fri, 26 Dec 1997 09:29:51 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Miyazaki",
"T.",
""
],
[
"Ohzeki",
"C.",
""
],
[
"Yamanobe",
"M.",
""
]
] | In the conventional $p$-brane theory, a gauge ($p+1$)-form field $\phi^{(p+1)}$ mediates the interaction between $p$-branes, which is gauge invariant in the sense $\phi^{(p+1)}\to \phi^{(p+1)}+d\Lambda^{(p)}$ with $\Lambda^{(p)}$, an arbitrary $p$-form and $d$, a boundary operator. We, on the contrary, propose to introduce a new gauge field $\phi^{(p+2)}$ mediating the interaction, and we have a new type of gauge transformation: $\phi^{(p+2)}\to \phi^{(p+2)} +\delta\Lambda^{(p+3)}$, with $\delta$, a coboundary operator. |
1608.07506 | Partha Mukhopadhyay | Partha Mukhopadhyay | General Construction of Tubular Geometry | 40 pages | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider the problem of locally describing tubular geometry around a
submanifold embedded in a (pseudo)Riemannian manifold in its general form.
Given the geometry of ambient space in an arbitrary coordinate system and
equations determining the submanifold in the same system, we compute the
tubular expansion coefficients in terms of this {\it a priori data}. This is
done by using an indirect method that crucially applies the tubular expansion
theorem for vielbein previously derived. With an explicit construction
involving the relevant coordinate and non-coordinate frames we verify
consistency of the whole method up to quadratic order in vielbein expansion.
Furthermore, we perform certain (long and tedious) higher order computation
which verifies the first non-trivial spin connection term in the expansion for
the first time. Earlier a similar method was used to compute tubular geometry
in loop space. We explain this work in the light of our general construction.
| [
{
"created": "Fri, 26 Aug 2016 16:26:11 GMT",
"version": "v1"
}
] | 2016-08-29 | [
[
"Mukhopadhyay",
"Partha",
""
]
] | We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction. |
hep-th/9705176 | Antti Niemi | L. Faddeev and A.J. Niemi | Toroidal Confugurations As Stable Solitons | 21 pages, 10 figures | null | null | null | hep-th | null | Previously we have proposed that in certain relativistic quantum field
theories knotlike configurations may appear as stable solitons. Here we present
a detailed investigation of the simplest knotted soliton, the torus-shaped
unknot.
| [
{
"created": "Thu, 22 May 1997 21:46:45 GMT",
"version": "v1"
}
] | 2009-09-25 | [
[
"Faddeev",
"L.",
""
],
[
"Niemi",
"A. J.",
""
]
] | Previously we have proposed that in certain relativistic quantum field theories knotlike configurations may appear as stable solitons. Here we present a detailed investigation of the simplest knotted soliton, the torus-shaped unknot. |
2310.07556 | Matheus Ara\'ujo Marques | M.A. Marques and R. Menezes | Geometrically constrained multifield models with BNRT solutions | v2; 13 pages, 7 figures; text and references added; accepted in
Chaos, Solitons and Fractals | Chaos, Solitons and Fractals 181 (2024) 114730 | 10.1016/j.chaos.2024.114730 | null | hep-th | http://creativecommons.org/licenses/by-nc-nd/4.0/ | In this paper, we investigate multifield models in which the two-field BNRT
model is coupled to a third field through mediator functions in the Lagrangian
density. To conduct the investigation, we obtain the equations of motion and
develop a first-order formalism based on energy minimization. Two possibilities
are considered: i) the third field acting in the mediator functions to modify
the BNRT solutions; ii) the BNRT fields feeding the mediator function to
produce effects in the kink solution of the third field. In the case i), the
results show that the solutions may be related to the standard ones with the
coordinate redefined in terms of the mediator functions if they are equal. This
allows to induce effects similar to geometric constrictions in the core, or to
compactify the tail of the BNRT solutions. If the mediator functions differ one
from another, we show that the effects are distinct, with the compactification
of just one of the two-field solutions. In the case ii), the orbit parameter of
the model plays an important role, modifying the mediator function that induces
changes in the profile of the kink associated to the third field.
| [
{
"created": "Wed, 11 Oct 2023 15:00:39 GMT",
"version": "v1"
},
{
"created": "Mon, 18 Mar 2024 14:24:46 GMT",
"version": "v2"
}
] | 2024-03-19 | [
[
"Marques",
"M. A.",
""
],
[
"Menezes",
"R.",
""
]
] | In this paper, we investigate multifield models in which the two-field BNRT model is coupled to a third field through mediator functions in the Lagrangian density. To conduct the investigation, we obtain the equations of motion and develop a first-order formalism based on energy minimization. Two possibilities are considered: i) the third field acting in the mediator functions to modify the BNRT solutions; ii) the BNRT fields feeding the mediator function to produce effects in the kink solution of the third field. In the case i), the results show that the solutions may be related to the standard ones with the coordinate redefined in terms of the mediator functions if they are equal. This allows to induce effects similar to geometric constrictions in the core, or to compactify the tail of the BNRT solutions. If the mediator functions differ one from another, we show that the effects are distinct, with the compactification of just one of the two-field solutions. In the case ii), the orbit parameter of the model plays an important role, modifying the mediator function that induces changes in the profile of the kink associated to the third field. |
hep-th/9612071 | null | E. Ragoucy | W-strings from N=2 Hamiltonian reduction and classification of N=2 super
W-algebras | Latex, 13 pages | null | null | null | hep-th | null | We present an algebraic approach to string theory, using a Hamiltonian
reduction of N=2 WZW models. An embedding of sl(1|2) in a Lie superalgebra
determines a niltopent subalgebra. Chirally gauging this subalgebra in the
corresponding WZW action leads to an extension of the N=2 superconformal
algebra. We classify all the embeddings of sl(1|2) into Lie superalgebras: this
provides an exhaustive classification and characterization of all extended N=2
superconformal algebras. Then, twisting these algebras, we obtain the BRST
structure of a string theory. We characterize and classify all the string
theories which can be obtained in this way.
Based on a common work of E. Ragoucy, A. Sevrin and P. Sorba, presented by E.
Ragoucy at ``Extended and Quantum Algebras and their Applications to Physics'',
Nankai Institute in Tianjin (China) August 19-24 1996
| [
{
"created": "Fri, 6 Dec 1996 15:20:41 GMT",
"version": "v1"
}
] | 2016-09-06 | [
[
"Ragoucy",
"E.",
""
]
] | We present an algebraic approach to string theory, using a Hamiltonian reduction of N=2 WZW models. An embedding of sl(1|2) in a Lie superalgebra determines a niltopent subalgebra. Chirally gauging this subalgebra in the corresponding WZW action leads to an extension of the N=2 superconformal algebra. We classify all the embeddings of sl(1|2) into Lie superalgebras: this provides an exhaustive classification and characterization of all extended N=2 superconformal algebras. Then, twisting these algebras, we obtain the BRST structure of a string theory. We characterize and classify all the string theories which can be obtained in this way. Based on a common work of E. Ragoucy, A. Sevrin and P. Sorba, presented by E. Ragoucy at ``Extended and Quantum Algebras and their Applications to Physics'', Nankai Institute in Tianjin (China) August 19-24 1996 |
1906.02619 | Enrico Olivucci | Gleb Arutyunov and Enrico Olivucci | Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction | 16 pages. The statement about coincidence of the Poisson structure of
spin variables at generic $N$ and $\ell$ with that of 1811.08727 was
corrected | null | null | null | hep-th math-ph math.MP nlin.SI | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We derive a Hamiltonian structure for the $N$-particle hyperbolic spin
Ruijsenaars-Schneider model by means of Poisson reduction of a suitable initial
phase space. This phase space is realised as the direct product of the
Heisenberg double of a factorisable Lie group with another symplectic manifold
that is a certain deformation of the standard canonical relations for $N\ell$
conjugate pairs of dynamical variables. We show that the model enjoys the
Poisson-Lie symmetry of the spin group ${\rm GL}_{\ell}({\mathbb C})$ which
explains its superintegrability. Our results are obtained in the formalism of
the classical $r$-matrix and they are compatible with the recent findings on
the different Hamiltonian structure of the model established in the framework
of the quasi-Hamiltonian reduction applied to a quasi-Poisson manifold.
| [
{
"created": "Thu, 6 Jun 2019 14:44:55 GMT",
"version": "v1"
},
{
"created": "Wed, 21 Aug 2019 09:10:42 GMT",
"version": "v2"
}
] | 2019-08-22 | [
[
"Arutyunov",
"Gleb",
""
],
[
"Olivucci",
"Enrico",
""
]
] | We derive a Hamiltonian structure for the $N$-particle hyperbolic spin Ruijsenaars-Schneider model by means of Poisson reduction of a suitable initial phase space. This phase space is realised as the direct product of the Heisenberg double of a factorisable Lie group with another symplectic manifold that is a certain deformation of the standard canonical relations for $N\ell$ conjugate pairs of dynamical variables. We show that the model enjoys the Poisson-Lie symmetry of the spin group ${\rm GL}_{\ell}({\mathbb C})$ which explains its superintegrability. Our results are obtained in the formalism of the classical $r$-matrix and they are compatible with the recent findings on the different Hamiltonian structure of the model established in the framework of the quasi-Hamiltonian reduction applied to a quasi-Poisson manifold. |
2112.07541 | Kaixin Ji | Kaixin Ji, Ling-Yan Hung | Information propagation in a non-local model with emergent locality | Slightly revised abstract, section 2, section 4.2 and discussion | null | 10.1007/JHEP04(2022)106 | null | hep-th cond-mat.str-el quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we revisit a "relatively local" model proposed in
arXiv:1811.07241, where locality and dimensionality of space only emerges from
the entanglement structure of the state the system is in. Various quantities
such as butterfly velocity/ entanglement speed can be defined similarly, at
least in the regime where locality is well defined and a light cone structure
emerges in the correlation between sites. We find that the relations observed
between them in local models arXiv:1908.06993 are not respected. In particular,
we conjecture that the hierarchy of the interaction over different distances
provides different "layers" of light-cones. When long range interactions are
sufficiently suppressed, the effective light cones are dominated by linear
behaviors with little remnant of non-locality. This could potentially be used
as a physical smoking gun for emergent locality in non-local models.
| [
{
"created": "Tue, 14 Dec 2021 16:51:26 GMT",
"version": "v1"
},
{
"created": "Sat, 22 Jan 2022 16:38:32 GMT",
"version": "v2"
},
{
"created": "Mon, 28 Mar 2022 09:38:19 GMT",
"version": "v3"
}
] | 2022-05-04 | [
[
"Ji",
"Kaixin",
""
],
[
"Hung",
"Ling-Yan",
""
]
] | In this paper, we revisit a "relatively local" model proposed in arXiv:1811.07241, where locality and dimensionality of space only emerges from the entanglement structure of the state the system is in. Various quantities such as butterfly velocity/ entanglement speed can be defined similarly, at least in the regime where locality is well defined and a light cone structure emerges in the correlation between sites. We find that the relations observed between them in local models arXiv:1908.06993 are not respected. In particular, we conjecture that the hierarchy of the interaction over different distances provides different "layers" of light-cones. When long range interactions are sufficiently suppressed, the effective light cones are dominated by linear behaviors with little remnant of non-locality. This could potentially be used as a physical smoking gun for emergent locality in non-local models. |
2211.01285 | Sudeepan Datta | B. Ananthanarayan, Sumit Banik, Souvik Bera, Sudeepan Datta | FeynGKZ: a Mathematica package for solving Feynman integrals using GKZ
hypergeometric systems | 26 pages, 1 figure, code repository:
https://github.com/anant-group/FeynGKZ | null | 10.1016/j.cpc.2023.108699 | null | hep-th hep-ph math-ph math.MP | http://creativecommons.org/licenses/by/4.0/ | In the Lee-Pomeransky representation, Feynman integrals can be identified as
a subset of Euler-Mellin integrals, which are known to satisfy
Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations.
Here we present an automated package to derive the associated GKZ system for a
given Feynman diagram and solve it in terms of hypergeometric functions using
two equivalent algorithms, namely the triangulation method and the Gr\"obner
deformation method. We present our code in the form of a Mathematica package
FeynGKZ.wl which requires the softwares polymake, Macaulay2 and TOPCOM, and the
packages AMBRE and Olsson.wl as dependencies. As applications of the package,
we find series solutions to the GKZ systems of several one-loop and two-loop
Feynman integrals. These are included in the file Examples.nb that can be
downloaded along with the package from https://github.com/anant-group/FeynGKZ.
| [
{
"created": "Wed, 2 Nov 2022 17:07:16 GMT",
"version": "v1"
}
] | 2023-03-22 | [
[
"Ananthanarayan",
"B.",
""
],
[
"Banik",
"Sumit",
""
],
[
"Bera",
"Souvik",
""
],
[
"Datta",
"Sudeepan",
""
]
] | In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. Here we present an automated package to derive the associated GKZ system for a given Feynman diagram and solve it in terms of hypergeometric functions using two equivalent algorithms, namely the triangulation method and the Gr\"obner deformation method. We present our code in the form of a Mathematica package FeynGKZ.wl which requires the softwares polymake, Macaulay2 and TOPCOM, and the packages AMBRE and Olsson.wl as dependencies. As applications of the package, we find series solutions to the GKZ systems of several one-loop and two-loop Feynman integrals. These are included in the file Examples.nb that can be downloaded along with the package from https://github.com/anant-group/FeynGKZ. |
0901.1646 | Murat Gunaydin | Murat Gunaydin and Oleksandr Pavlyk | Spectrum Generating Conformal and Quasiconformal U-Duality Groups,
Supergravity and Spherical Vectors | Section 4 is split with the addition of a subsection on quadratic
Casimir operators; references added; typos corrected. Latex file; 53 pages | JHEP 1004:070,2010 | 10.1007/JHEP04(2010)070 | null | hep-th gr-qc math-ph math.MP math.RT | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | After reviewing the algebraic structures that underlie the geometries of N=2
Maxwell-Einstein supergravity theories (MESGT) in five and four dimensions with
symmetric scalar manifolds, we give a unified realization of their three
dimensional U-duality groups as spectrum generating quasiconformal groups. They
are F_{4(4)}, E_{6(2)}, E_{7(-5)}, E_{8(-24)} and SO(n+2,4). Our formulation is
covariant with respect to U-duality symmetry groups of corresponding five
dimensional supergravity theories, which are SL(3,R), SL(3,C), SU*(6), E_{6(6)}
and SO(n-1,1)X SO(1,1), respectively. We determine the spherical vectors of
quasiconformal realizations of all these groups twisted by a unitary character.
We also give their quadratic Casimir operators and determine their values. Our
work lays the algebraic groundwork for constructing the unitary representations
of these groups induced by their geometric quasiconformal actions, which
include the quaternionic discrete series. For rank 2 cases, SU(2,1) and
G_{2(2)}, corresponding to simple N=2 supergravity in four and five dimensions,
this program was carried out in arXiv:0707.1669. We also discuss the
corresponding algebraic structures underlying symmetries of matter coupled N=4
and N>4 supergravity theories. They lead to quasiconformal realizations of
split real forms of U-duality groups as a straightforward extension of the
quaternionic real forms.
| [
{
"created": "Mon, 12 Jan 2009 19:38:38 GMT",
"version": "v1"
},
{
"created": "Mon, 2 Mar 2009 02:16:51 GMT",
"version": "v2"
}
] | 2014-11-18 | [
[
"Gunaydin",
"Murat",
""
],
[
"Pavlyk",
"Oleksandr",
""
]
] | After reviewing the algebraic structures that underlie the geometries of N=2 Maxwell-Einstein supergravity theories (MESGT) in five and four dimensions with symmetric scalar manifolds, we give a unified realization of their three dimensional U-duality groups as spectrum generating quasiconformal groups. They are F_{4(4)}, E_{6(2)}, E_{7(-5)}, E_{8(-24)} and SO(n+2,4). Our formulation is covariant with respect to U-duality symmetry groups of corresponding five dimensional supergravity theories, which are SL(3,R), SL(3,C), SU*(6), E_{6(6)} and SO(n-1,1)X SO(1,1), respectively. We determine the spherical vectors of quasiconformal realizations of all these groups twisted by a unitary character. We also give their quadratic Casimir operators and determine their values. Our work lays the algebraic groundwork for constructing the unitary representations of these groups induced by their geometric quasiconformal actions, which include the quaternionic discrete series. For rank 2 cases, SU(2,1) and G_{2(2)}, corresponding to simple N=2 supergravity in four and five dimensions, this program was carried out in arXiv:0707.1669. We also discuss the corresponding algebraic structures underlying symmetries of matter coupled N=4 and N>4 supergravity theories. They lead to quasiconformal realizations of split real forms of U-duality groups as a straightforward extension of the quaternionic real forms. |
hep-th/0407079 | Hossein Yavartanoo | Hossein Yavartanoo | Cosmological Solution from D-brane motion in NS5-Branes background | 15 pages, To appear in International Journal of Modern Physics A | Int.J.Mod.Phys. A20 (2005) 7633-7645 | 10.1142/S0217751X05022329 | null | hep-th | null | We study dynamics of a D3-brane propagating in the vicinity of k coincident
NS5 branes. We show that when $g_s$ is small, there exists a regime in which
dynamics of the D-brane is governed by Dirac-Born-Infeld action while higher
order derivative in the expansion can not be neglected. This leads to a
restriction on how fast scalar field may roll. We analyze the motion of a
rolling scalar field in this regime, and extend the analysis to cosmological
systems obtained by coupling this type of field theory to four dimensinal
gravity. It also leads to some FRW cosmologies, some of which are related to
those obtained with tachyon matter.
| [
{
"created": "Sat, 10 Jul 2004 22:26:40 GMT",
"version": "v1"
},
{
"created": "Sun, 18 Jul 2004 16:41:54 GMT",
"version": "v2"
},
{
"created": "Mon, 20 Sep 2004 16:46:10 GMT",
"version": "v3"
},
{
"created": "Wed, 13 Apr 2005 07:27:37 GMT",
"version": "v4"
}
] | 2009-11-10 | [
[
"Yavartanoo",
"Hossein",
""
]
] | We study dynamics of a D3-brane propagating in the vicinity of k coincident NS5 branes. We show that when $g_s$ is small, there exists a regime in which dynamics of the D-brane is governed by Dirac-Born-Infeld action while higher order derivative in the expansion can not be neglected. This leads to a restriction on how fast scalar field may roll. We analyze the motion of a rolling scalar field in this regime, and extend the analysis to cosmological systems obtained by coupling this type of field theory to four dimensinal gravity. It also leads to some FRW cosmologies, some of which are related to those obtained with tachyon matter. |
2307.06929 | Juan Mauricio Valencia Villegas | S. Mironov and M. Valencia-Villegas | Stability of nonsingular cosmologies in Galileon models with torsion. A
no-go theorem for eternal subluminality | 8 pages, 4 figures. Matches the version accepted for publication in
PRD. Added clarifying comments in the proof of the No-Go, references added,
results unchanged | Phys. Rev. D, 109, 2024, 044-073 | 10.1103/PhysRevD.109.044073 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Generic models in Galileons or Horndeski theory do not have cosmological
solutions that are free of instabilities and singularities in the entire time
of evolution. We extend this No-Go theorem to a spacetime with torsion. On this
more general geometry the No-Go argument now holds provided the additional
hypothesis that the graviton is also subluminal throughout the entire
evolution. Thus, critically different for Galileons' stability on a torsionful
spacetime, an arguably unphysical although arbitrarily short (deep UV) phase
occurring at an arbitrary time, when the speed of gravity $(c_g)$ is slightly
higher than luminal $(c)$, and by at least an amount $c_g\geq \,\sqrt{2}\,c $,
can lead to an all-time linearly stable and nonsingular cosmology. As a proof
of principle we build a stable model for a cosmological bounce that is almost
always subluminal, where the short-lived superluminal phase occurs before the
bounce and that transits to General Relativity in the asymptotic past and
future.
| [
{
"created": "Thu, 13 Jul 2023 17:51:48 GMT",
"version": "v1"
},
{
"created": "Mon, 5 Feb 2024 07:01:14 GMT",
"version": "v2"
}
] | 2024-07-22 | [
[
"Mironov",
"S.",
""
],
[
"Valencia-Villegas",
"M.",
""
]
] | Generic models in Galileons or Horndeski theory do not have cosmological solutions that are free of instabilities and singularities in the entire time of evolution. We extend this No-Go theorem to a spacetime with torsion. On this more general geometry the No-Go argument now holds provided the additional hypothesis that the graviton is also subluminal throughout the entire evolution. Thus, critically different for Galileons' stability on a torsionful spacetime, an arguably unphysical although arbitrarily short (deep UV) phase occurring at an arbitrary time, when the speed of gravity $(c_g)$ is slightly higher than luminal $(c)$, and by at least an amount $c_g\geq \,\sqrt{2}\,c $, can lead to an all-time linearly stable and nonsingular cosmology. As a proof of principle we build a stable model for a cosmological bounce that is almost always subluminal, where the short-lived superluminal phase occurs before the bounce and that transits to General Relativity in the asymptotic past and future. |
hep-th/9209025 | null | Sumit R. Das and S. Kalyana Rama | Renormalization of Couplings in Embedded Random Surfaces | 14 pages. Preprint TIFR-TH-92/48 | Mod.Phys.Lett. A7 (1992) 3747-3758 | 10.1142/S0217732392003165 | null | hep-th | null | We study the dressing of operators and flows of corresponding couplings in
models of {\it embedded} random surfaces. We show that these dressings can be
obtained by applying the methods of David and Distler and Kawai. We consider
two extreme limits. In the first limit the string tension is large and the
dynamics is dominated by the Nambu-Goto term. We analyze this theory around a
classical solution in the situation where the length scale of the solution is
large compared to the length scale set by the string tension. Couplings get
dressed by the liouville mode (which is now a composite field) in a non-trivial
fashion. However this does {\it not} imply that the excitations around a
physical ``long string" have a phase space corresponding to an extra dimension.
In the second limit the string tension is small and the dynamics is governed by
the extrinsic curvature term. We show, perturbatively, that in this theory the
relationship between the induced metric and the worldsheet metric is
``renormalized", while the extrinsic curvature term receives a non-trivial
dressing as well. This has the consequence that in a generic situation the
dependence of couplings on the physical scale is different from that predicted
by their beta functions.
| [
{
"created": "Tue, 8 Sep 1992 20:08:00 GMT",
"version": "v1"
}
] | 2015-06-26 | [
[
"Das",
"Sumit R.",
""
],
[
"Rama",
"S. Kalyana",
""
]
] | We study the dressing of operators and flows of corresponding couplings in models of {\it embedded} random surfaces. We show that these dressings can be obtained by applying the methods of David and Distler and Kawai. We consider two extreme limits. In the first limit the string tension is large and the dynamics is dominated by the Nambu-Goto term. We analyze this theory around a classical solution in the situation where the length scale of the solution is large compared to the length scale set by the string tension. Couplings get dressed by the liouville mode (which is now a composite field) in a non-trivial fashion. However this does {\it not} imply that the excitations around a physical ``long string" have a phase space corresponding to an extra dimension. In the second limit the string tension is small and the dynamics is governed by the extrinsic curvature term. We show, perturbatively, that in this theory the relationship between the induced metric and the worldsheet metric is ``renormalized", while the extrinsic curvature term receives a non-trivial dressing as well. This has the consequence that in a generic situation the dependence of couplings on the physical scale is different from that predicted by their beta functions. |
1301.7498 | Reinhard Alkofer | Valentin Mader and Reinhard Alkofer | Including four-gluon interactions into Landau and maximally-Abelian
gauge Dyson-Schwinger studies | 8 pages, 3 figures, talk presented at the Xth Quark Confinement and
the Hadron Spectrum, Munich, Germany, 2012 | PoS Confinement X (2013) 063 | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In Dyson-Schwinger studies of the Yang-Mills propagators the four-gluon
interaction has been usually neglected due to the related technical
difficulties with the associated two-loop terms and especially their
renormalization. A possible scenario to renormalize these fully-dressed
two-loop terms is presented. Preliminary results for the Landau gauge gluon
propagator are shown. Implications for the gluon propagators in maximally
Abelian gauge are discussed.
| [
{
"created": "Thu, 31 Jan 2013 02:48:24 GMT",
"version": "v1"
},
{
"created": "Fri, 1 Feb 2013 23:40:37 GMT",
"version": "v2"
}
] | 2013-02-05 | [
[
"Mader",
"Valentin",
""
],
[
"Alkofer",
"Reinhard",
""
]
] | In Dyson-Schwinger studies of the Yang-Mills propagators the four-gluon interaction has been usually neglected due to the related technical difficulties with the associated two-loop terms and especially their renormalization. A possible scenario to renormalize these fully-dressed two-loop terms is presented. Preliminary results for the Landau gauge gluon propagator are shown. Implications for the gluon propagators in maximally Abelian gauge are discussed. |
hep-th/9208007 | Shahn Majid | Tomasz Brzezinski and Shahn Majid | Quantum group gauge theory on quantum spaces | 65 pages DAMTP/92-27 Revised to emphasise more the U(1) monopole
example -- includes now full details in the 3D differential calculus | Commun.Math.Phys. 157 (1993) 591-638; Erratum-ibid. 167 (1995) 235 | 10.1007/BF02096884 | null | hep-th | null | We construct quantum group-valued canonical connections on quantum
homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere
of Podles quantum differential coming from the 3-D calculus of Woronowicz on
$SU_q(2)$ . The construction is presented within the setting of a general
theory of quantum principal bundles with quantum group (Hopf algebra) fiber,
associated quantum vector bundles and connection one-forms. Both the base space
(spacetime) and the total space are non-commutative algebras (quantum spaces).
| [
{
"created": "Mon, 3 Aug 1992 12:00:44 GMT",
"version": "v1"
},
{
"created": "Fri, 26 Mar 1993 16:50:34 GMT",
"version": "v2"
}
] | 2009-10-22 | [
[
"Brzezinski",
"Tomasz",
""
],
[
"Majid",
"Shahn",
""
]
] | We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces). |
1906.10383 | Masao Jinzenji | Masao Jinzenji (Okayama University), Ken Kuwata (Hokkaido University) | Holomorphic Vector Field and Topological Sigma Model on CP^1 World Sheet | 32 pages, revised version for publication in IJMPA | International Journal of Modern Physics A Vol. 35, No. 30, 2050192
(2020) | 10.1142/S0217751X20501924 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Witten suggested that fixed-point theorems can be derived by the
supersymmetric sigma model on a Riemann manifold M with potential term induced
from Killing vector on M. One of the well-known fixed-point theorem is the Bott
residue formula which represents intersection number of Chern classes of
holomorphic vector bundles on a Kahler manifold M as sum of contributions from
fixed point sets of a holomorphic vector field K on M. In this paper, we derive
the Bott residue formula by using topological sigma model (A-model) that
describes dynamics of maps from CP^{1} to M, with potential term induced from
the vector field $K$. Our strategy is to restrict phase space of path integral
to maps homotopic to constant maps. As an effect of adding a potential term to
topological sigma model, we are forced to modify BRST symmetry of the original
topological sigma model. Our potential term and BRST symmetry are closely
related to the idea used in the paper by Beasley and Witten where potential
terms induced from holomorphic section of a holomorphic vector bundle and
corresponding supersymmetry are considered.
| [
{
"created": "Tue, 25 Jun 2019 08:42:12 GMT",
"version": "v1"
},
{
"created": "Tue, 2 Jul 2019 06:35:55 GMT",
"version": "v2"
},
{
"created": "Mon, 12 Oct 2020 06:05:42 GMT",
"version": "v3"
}
] | 2020-11-03 | [
[
"Jinzenji",
"Masao",
"",
"Okayama University"
],
[
"Kuwata",
"Ken",
"",
"Hokkaido University"
]
] | Witten suggested that fixed-point theorems can be derived by the supersymmetric sigma model on a Riemann manifold M with potential term induced from Killing vector on M. One of the well-known fixed-point theorem is the Bott residue formula which represents intersection number of Chern classes of holomorphic vector bundles on a Kahler manifold M as sum of contributions from fixed point sets of a holomorphic vector field K on M. In this paper, we derive the Bott residue formula by using topological sigma model (A-model) that describes dynamics of maps from CP^{1} to M, with potential term induced from the vector field $K$. Our strategy is to restrict phase space of path integral to maps homotopic to constant maps. As an effect of adding a potential term to topological sigma model, we are forced to modify BRST symmetry of the original topological sigma model. Our potential term and BRST symmetry are closely related to the idea used in the paper by Beasley and Witten where potential terms induced from holomorphic section of a holomorphic vector bundle and corresponding supersymmetry are considered. |
hep-th/9307186 | Deogki Hong | D. K. Hong and S. H. Park | Large-N analysis of (2+1)-dimensional Thirring model | 14 pages Latex. (Revised version: some changes have been made and
references added.) To appear in Phys. Rev. D, SNUTP 93-47 | Phys.Rev. D49 (1994) 5507-5511 | 10.1103/PhysRevD.49.5507 | null | hep-th | null | We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction
(Thirring) model in the framework of the $1/N$ expansion. By solving the
Dyson-Schwinger equation in the large-$N$ limit, we show that in the
two-component formalism the fermions acquire parity-violating mass dynamically
in the range of the dimensionless coupling $\alpha$, $0 \leq \alpha \leq
\alpha_c \equiv {1\over16} {\rm exp} (- {N \pi^2 \over 16})$. The symmetry
breaking pattern is, however, in a way to conserve the overall parity of the
theory such that the Chern-Simons term is not induced at any orders in $1/N$.
$\alpha_c$ turns out to be a non-perturbative UV-fixed point in $1/N$. The
$\beta$ function is calculated to be $\beta (\alpha) = -2 (\alpha - \alpha_c)$
near the fixed point, and the UV-fixed point and the $\beta$ function are shown
exact in the $1/N$ expansion.
| [
{
"created": "Fri, 30 Jul 1993 07:10:24 GMT",
"version": "v1"
},
{
"created": "Tue, 10 May 1994 18:53:29 GMT",
"version": "v2"
}
] | 2009-10-22 | [
[
"Hong",
"D. K.",
""
],
[
"Park",
"S. H.",
""
]
] | We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism the fermions acquire parity-violating mass dynamically in the range of the dimensionless coupling $\alpha$, $0 \leq \alpha \leq \alpha_c \equiv {1\over16} {\rm exp} (- {N \pi^2 \over 16})$. The symmetry breaking pattern is, however, in a way to conserve the overall parity of the theory such that the Chern-Simons term is not induced at any orders in $1/N$. $\alpha_c$ turns out to be a non-perturbative UV-fixed point in $1/N$. The $\beta$ function is calculated to be $\beta (\alpha) = -2 (\alpha - \alpha_c)$ near the fixed point, and the UV-fixed point and the $\beta$ function are shown exact in the $1/N$ expansion. |
1312.2626 | James Lucietti | Carmen Li, James Lucietti | Three-dimensional black holes and descendants | 10 pages. v2: general solution has second Killing field, changes and
additions to reflect this, references added. v3: included analysis of
non-extreme solution and discussion | Phys. Lett. B 738 (2014) , 48-4 | 10.1016/j.physletb.2014.09.012 | EMPG-13-22 | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We determine the most general three-dimensional vacuum spacetime with a
negative cosmological constant containing a non-singular Killing horizon. We
show that the general solution with a spatially compact horizon possesses a
second commuting Killing field and deduce that it must be related to the BTZ
black hole (or its near-horizon geometry) by a diffeomorphism. We show there is
a general class of asymptotically AdS$_3$ extreme black holes with arbitrary
charges with respect to one of the asymptotic-symmetry Virasoro algebras and
vanishing charges with respect to the other. We interpret these as descendants
of the extreme BTZ black hole.
| [
{
"created": "Mon, 9 Dec 2013 23:05:23 GMT",
"version": "v1"
},
{
"created": "Thu, 19 Dec 2013 19:27:37 GMT",
"version": "v2"
},
{
"created": "Tue, 11 Feb 2014 20:25:09 GMT",
"version": "v3"
}
] | 2014-09-24 | [
[
"Li",
"Carmen",
""
],
[
"Lucietti",
"James",
""
]
] | We determine the most general three-dimensional vacuum spacetime with a negative cosmological constant containing a non-singular Killing horizon. We show that the general solution with a spatially compact horizon possesses a second commuting Killing field and deduce that it must be related to the BTZ black hole (or its near-horizon geometry) by a diffeomorphism. We show there is a general class of asymptotically AdS$_3$ extreme black holes with arbitrary charges with respect to one of the asymptotic-symmetry Virasoro algebras and vanishing charges with respect to the other. We interpret these as descendants of the extreme BTZ black hole. |
1503.07457 | Watse Sybesma | Watse Sybesma and Stefan Vandoren | Lifshitz quasinormal modes and relaxation from holography | 16 pages and 5 figures | null | 10.1007/JHEP05(2015)021 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We obtain relaxation times for field theories with Lifshitz scaling and with
holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by
computing quasinormal modes of a bulk scalar field in the presence of Lifshitz
black branes. We determine the relation between relaxation time and dynamical
exponent z, for various values of boundary dimension d and operator scaling
dimension. It is found that for d>z+1, at zero momenta, the modes are
non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1
and zero momenta, we present analytical results.
| [
{
"created": "Wed, 25 Mar 2015 17:01:56 GMT",
"version": "v1"
}
] | 2015-06-11 | [
[
"Sybesma",
"Watse",
""
],
[
"Vandoren",
"Stefan",
""
]
] | We obtain relaxation times for field theories with Lifshitz scaling and with holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by computing quasinormal modes of a bulk scalar field in the presence of Lifshitz black branes. We determine the relation between relaxation time and dynamical exponent z, for various values of boundary dimension d and operator scaling dimension. It is found that for d>z+1, at zero momenta, the modes are non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1 and zero momenta, we present analytical results. |
1507.04190 | Vincent Rivasseau | Vincent Rivasseau | Why are tensor field theories asymptotically free? | 8 pages, 3 figures | null | 10.1209/0295-5075/111/60011 | null | hep-th math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this pedagogic letter we explain the combinatorics underlying the generic
asymptotic freedom of tensor field theories. We focus on simple combinatorial
models with a $1/p^2$ propagator and quartic interactions and on the comparison
between the intermediate field representations of the vector, matrix and tensor
cases. The transition from asymptotic freedom (tensor case) to asymptotic
safety (matrix case) is related to the crossing symmetry of the matrix vertex
whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as
in the ordinary scalar case, is simply due to the absence of any wave function
renormalization at one loop.
| [
{
"created": "Wed, 15 Jul 2015 12:38:31 GMT",
"version": "v1"
}
] | 2015-10-28 | [
[
"Rivasseau",
"Vincent",
""
]
] | In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar case, is simply due to the absence of any wave function renormalization at one loop. |
2306.13663 | Dimitrios Metaxas | Dimitrios Metaxas | The quantum Yang-Mills theory | 16 pages, comments and references added | null | null | null | hep-th quant-ph | http://creativecommons.org/licenses/by/4.0/ | In axiomatic quantum field theory, the postulate of the uniqueness of the
vacuum (a pure vacuum state) is independent of the other axioms and equivalent
to the cluster decomposition property. The latter, however, implies a Coulomb
or Yukawa attenuation of the interactions at growing distance, hence cannot
accomodate the confining properties of the strong interaction. The solution of
the Yang-Mills quantum theory given previously, uses an auxiliary field to
incorporate Gauss's law, and demonstrates the existence of two separate vacua,
the perturbative and the confining vacuum, therefore a mixed vacuum state,
deriving confinement, as well as the related, expected properties of the strong
interaction. The existence of multiple vacua is, in fact, expected by the
axiomatic, algebraic quantum field theory, via the decomposition of the vacuum
state to eigenspaces of the auxiliary field. The general vacuum state is a
mixed quantum state and the cluster decomposition property does not hold.
Because of the energy density difference between the two vacua, the physics of
the strong interactions does not admit a Lagrangian description. I clarify the
above remarks related to the previous solution of the Yang-Mills interaction,
and conclude with some discussion, a criticism of a related mathematical
problem, and some tentative comments regarding the spin-2 case.
| [
{
"created": "Sun, 11 Jun 2023 15:03:45 GMT",
"version": "v1"
},
{
"created": "Wed, 20 Sep 2023 11:58:23 GMT",
"version": "v2"
}
] | 2023-09-21 | [
[
"Metaxas",
"Dimitrios",
""
]
] | In axiomatic quantum field theory, the postulate of the uniqueness of the vacuum (a pure vacuum state) is independent of the other axioms and equivalent to the cluster decomposition property. The latter, however, implies a Coulomb or Yukawa attenuation of the interactions at growing distance, hence cannot accomodate the confining properties of the strong interaction. The solution of the Yang-Mills quantum theory given previously, uses an auxiliary field to incorporate Gauss's law, and demonstrates the existence of two separate vacua, the perturbative and the confining vacuum, therefore a mixed vacuum state, deriving confinement, as well as the related, expected properties of the strong interaction. The existence of multiple vacua is, in fact, expected by the axiomatic, algebraic quantum field theory, via the decomposition of the vacuum state to eigenspaces of the auxiliary field. The general vacuum state is a mixed quantum state and the cluster decomposition property does not hold. Because of the energy density difference between the two vacua, the physics of the strong interactions does not admit a Lagrangian description. I clarify the above remarks related to the previous solution of the Yang-Mills interaction, and conclude with some discussion, a criticism of a related mathematical problem, and some tentative comments regarding the spin-2 case. |
1310.4319 | Alfonso V. Ramallo | Alfonso V. Ramallo | Introduction to the AdS/CFT correspondence | 64 pages, 12 figures;v2: minor improvements;v3: references added | null | null | null | hep-th cond-mat.str-el hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This is a pedagogical introduction to the AdS/CFT correspondence, based on
lectures delivered by the author at the third IDPASC school. Starting with the
conceptual basis of the holographic dualities, the subject is developed
emphasizing some concrete topics, which are discussed in detail. A very brief
introduction to string theory is provided, containing the minimal ingredients
to understand the origin of the AdS/CFT duality. Other topics covered are the
holographic calculation of correlation functions, quark-antiquark potentials
and transport coefficients.
| [
{
"created": "Wed, 16 Oct 2013 10:15:33 GMT",
"version": "v1"
},
{
"created": "Thu, 17 Oct 2013 19:35:09 GMT",
"version": "v2"
},
{
"created": "Fri, 1 Nov 2013 18:23:13 GMT",
"version": "v3"
}
] | 2013-11-04 | [
[
"Ramallo",
"Alfonso V.",
""
]
] | This is a pedagogical introduction to the AdS/CFT correspondence, based on lectures delivered by the author at the third IDPASC school. Starting with the conceptual basis of the holographic dualities, the subject is developed emphasizing some concrete topics, which are discussed in detail. A very brief introduction to string theory is provided, containing the minimal ingredients to understand the origin of the AdS/CFT duality. Other topics covered are the holographic calculation of correlation functions, quark-antiquark potentials and transport coefficients. |
hep-th/9307141 | Nicholas Philip Warner | D. Nemeschansky and N.P. Warner | Off-Critical Lattice Analogues of $N=2$ Supersymmetric Quantum
Integrable Models | 27 pages and 2 figures, harvmac | Nucl.Phys. B413 (1994) 629-652 | 10.1016/0550-3213(94)90005-1 | null | hep-th cond-mat | null | We obtain off-critical (elliptic) Boltzmann weights for lattice models whose
continuum limits correspond to massive, $N=2$ supersymmetric, quantum
integrable field theories. We also compute the free energies of these models
and show that they are analytic in the region of parameter space where we
believe that the supersymmetry is unbroken. While the supersymmetry is not
directly realized on the lattice, there is still a very close connection
between the models described here and topological lattice models. A simple
example is discussed in detail and some corner transfer matrix computations are
also presented.
| [
{
"created": "Thu, 22 Jul 1993 22:16:08 GMT",
"version": "v1"
}
] | 2009-10-22 | [
[
"Nemeschansky",
"D.",
""
],
[
"Warner",
"N. P.",
""
]
] | We obtain off-critical (elliptic) Boltzmann weights for lattice models whose continuum limits correspond to massive, $N=2$ supersymmetric, quantum integrable field theories. We also compute the free energies of these models and show that they are analytic in the region of parameter space where we believe that the supersymmetry is unbroken. While the supersymmetry is not directly realized on the lattice, there is still a very close connection between the models described here and topological lattice models. A simple example is discussed in detail and some corner transfer matrix computations are also presented. |
hep-th/0005099 | Dmitri Vladimirovich Galtsov | V.V.Dyadichev and D.V.Gal'tsov | Solitons and black holes in non-Abelian Einstein-Born-Infeld theory | Latex, 9 pages, 9 eps figures | Phys.Lett. B486 (2000) 431-442 | 10.1016/S0370-2693(00)00713-9 | DTP-MSU/00-05 | hep-th | null | Recently it was shown that the Born-Infeld-type modification of the quadratic
Yang-Mills action gives rise to classical particle-like solutions in the flat
space which have a striking similarity with the Bartnik-McKinnon solutions
known in the gravity coupled Yang-Mills theory. We show that both families are
continuously related within the framework of the Einstein-Born-Infeld theory
through interpolating sequences of parameters. We also investigate an internal
structure of the associated black holes. It is found that the Born-Infeld
non-linearity leads to a drastic modification of the black hole interior
typical for the usual Yang-Mills theory. In the latter case a generic solution
exhibits violent metric oscillations near the singularity. In the Born-Infeld
case a generic interior solution is smooth, the metric has the standard
Schwarzschild type singularity, and we did not observe internal horizons. Such
smoothing of the 'violent' EYM singularity may be interpreted as a result of
quantum effects.
| [
{
"created": "Wed, 10 May 2000 21:59:07 GMT",
"version": "v1"
}
] | 2016-09-06 | [
[
"Dyadichev",
"V. V.",
""
],
[
"Gal'tsov",
"D. V.",
""
]
] | Recently it was shown that the Born-Infeld-type modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions known in the gravity coupled Yang-Mills theory. We show that both families are continuously related within the framework of the Einstein-Born-Infeld theory through interpolating sequences of parameters. We also investigate an internal structure of the associated black holes. It is found that the Born-Infeld non-linearity leads to a drastic modification of the black hole interior typical for the usual Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case a generic interior solution is smooth, the metric has the standard Schwarzschild type singularity, and we did not observe internal horizons. Such smoothing of the 'violent' EYM singularity may be interpreted as a result of quantum effects. |
1701.05229 | Sergei Parkhomenko | S.E. Parkhomenko | Generalized K\"ahler Geometry and current algebras in $SU(2)\times U(1)$
N=2 superconformal WZW model | 10 pages, misprints corrections | Mod. Phys. Lett. A, Vol. 32, No. 13 (2017) | 10.1142/S0217732317500766 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We examine the Generalized K$\ddot{a}$hler Geometry of quantum N=2
superconformal WZW model on $SU(2)\times U(1)$ and relate the right-moving and
left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler
Geometry data of the group manifold using Hamiltonian formalism.
| [
{
"created": "Wed, 18 Jan 2017 20:51:02 GMT",
"version": "v1"
},
{
"created": "Sat, 21 Jan 2017 11:09:45 GMT",
"version": "v2"
},
{
"created": "Wed, 5 Apr 2017 09:55:07 GMT",
"version": "v3"
},
{
"created": "Sun, 23 Apr 2017 16:08:54 GMT",
"version": "v4"
}
] | 2018-01-11 | [
[
"Parkhomenko",
"S. E.",
""
]
] | We examine the Generalized K$\ddot{a}$hler Geometry of quantum N=2 superconformal WZW model on $SU(2)\times U(1)$ and relate the right-moving and left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler Geometry data of the group manifold using Hamiltonian formalism. |
hep-th/0511267 | Hitoshi Nishino | Hitoshi Nishino and Subhash Rajpoot | Interacting Vector-Spinor and Nilpotent Supersymmetry | 10 pages, no figures | Class.Quant.Grav.23:5215-5226,2006 | 10.1088/0264-9381/23/17/007 | CSULB-PA-05-3 | hep-th | null | We formulate an interacting theory of a vector-spinor field that gauges
anticommuting spinor charges \{Q_\alpha{}^I, Q_\beta{}^J \} = 0 in arbitrary
space-time dimensions. The field content of the system is (\psi_\mu{}^{\alpha
I}, \chi^{\alpha I J}, A_\mu{}^I), where \psi_\mu{}^{\alpha I} is a
vector-spinor in the adjoint representation of an arbitrary gauge group, and
A_\mu{}^I is its gauge field, while \chi^{\alpha I J} is an extra spinor with
antisymmetric adjoint indices I J. Amazingly, the consistency of the
vector-spinor field equation is maintained, despite its non-trivial
interactions.
| [
{
"created": "Sat, 26 Nov 2005 07:20:51 GMT",
"version": "v1"
}
] | 2009-11-11 | [
[
"Nishino",
"Hitoshi",
""
],
[
"Rajpoot",
"Subhash",
""
]
] | We formulate an interacting theory of a vector-spinor field that gauges anticommuting spinor charges \{Q_\alpha{}^I, Q_\beta{}^J \} = 0 in arbitrary space-time dimensions. The field content of the system is (\psi_\mu{}^{\alpha I}, \chi^{\alpha I J}, A_\mu{}^I), where \psi_\mu{}^{\alpha I} is a vector-spinor in the adjoint representation of an arbitrary gauge group, and A_\mu{}^I is its gauge field, while \chi^{\alpha I J} is an extra spinor with antisymmetric adjoint indices I J. Amazingly, the consistency of the vector-spinor field equation is maintained, despite its non-trivial interactions. |
hep-th/0509120 | Nathan Berkovits | Nathan Berkovits (IFT-UNESP, Sao Paulo) | Pure Spinor Formalism as an N=2 Topological String | 34 pages harvmac tex | JHEP0510:089,2005 | 10.1088/1126-6708/2005/10/089 | IFT-P.031/2005 | hep-th | null | Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are
added to the pure spinor formalism for the superstring. Twisted $\hat c$=3 N=2
generators are then constructed where the pure spinor BRST operator is the
fermionic spin-one generator, and the formalism is interpreted as a critical
topological string. Three applications of this topological string theory
include the super-Poincare covariant computation of multiloop superstring
amplitudes without picture-changing operators, the construction of a cubic open
superstring field theory without contact-term problems, and a new
four-dimensional version of the pure spinor formalism which computes F-terms in
the spacetime action.
| [
{
"created": "Thu, 15 Sep 2005 18:54:07 GMT",
"version": "v1"
}
] | 2009-11-11 | [
[
"Berkovits",
"Nathan",
"",
"IFT-UNESP, Sao Paulo"
]
] | Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted $\hat c$=3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action. |
2107.03910 | Pietro Dall'Olio | Pietro Dall'Olio, Tim De Meerleer, David Dudal, Silvio Paolo Sorella,
Adnan Bashir | Landau-Khalatnikov-Fradkin transformations for the two loop massless
quark propagator | arXiv admin note: text overlap with arXiv:1911.01907 Correcting
typos. We added a few comments and the diagrammatic representation of the
Feynman rules, according to the referee's requests | null | 10.1016/j.nuclphysb.2021.115606 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence
of correlation functions within the class of linear covariant gauges. We derive
the LKFT for the quark propagator and explicitly evaluate it up to the two loop
level in the chiral limit. Although the number of diagrams to be evaluated is
significantly larger than with the conventional computational scheme, the
diagrams are simpler in nature, thereby leading to a considerably faster
evaluation of the gauge dependent part than naively expected. Finally, we also
resum the LKFT generated terms and compare our results with earlier work in the
literature.
| [
{
"created": "Thu, 8 Jul 2021 15:41:22 GMT",
"version": "v1"
},
{
"created": "Mon, 12 Jul 2021 14:39:52 GMT",
"version": "v2"
},
{
"created": "Wed, 3 Nov 2021 16:56:07 GMT",
"version": "v3"
}
] | 2021-11-24 | [
[
"Dall'Olio",
"Pietro",
""
],
[
"De Meerleer",
"Tim",
""
],
[
"Dudal",
"David",
""
],
[
"Sorella",
"Silvio Paolo",
""
],
[
"Bashir",
"Adnan",
""
]
] | Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation functions within the class of linear covariant gauges. We derive the LKFT for the quark propagator and explicitly evaluate it up to the two loop level in the chiral limit. Although the number of diagrams to be evaluated is significantly larger than with the conventional computational scheme, the diagrams are simpler in nature, thereby leading to a considerably faster evaluation of the gauge dependent part than naively expected. Finally, we also resum the LKFT generated terms and compare our results with earlier work in the literature. |
hep-th/9502164 | Giovanni Felder | Giovanni Felder, Alexander Varchenko | Remarks on the structure constants of the Verlinde algebra associated to
$sl_3$ | 5 pages, AmsTeX, 1 figure available on request | Lett.Math.Phys.37:167-171,1996 | 10.1007/BF00416019 | null | hep-th | null | The structure constants $N_{\lambda, \mu}^{\mu+\nu}$ of the $sl_2$ Verlinde
algebra as functions of $\mu$ either vanish or can be expressed after a change
of variable as the weight function of an irreducible representation of $sl_2$.
We give a similar formula in the $sl_3$ case.
| [
{
"created": "Tue, 28 Feb 1995 13:03:10 GMT",
"version": "v1"
}
] | 2016-09-06 | [
[
"Felder",
"Giovanni",
""
],
[
"Varchenko",
"Alexander",
""
]
] | The structure constants $N_{\lambda, \mu}^{\mu+\nu}$ of the $sl_2$ Verlinde algebra as functions of $\mu$ either vanish or can be expressed after a change of variable as the weight function of an irreducible representation of $sl_2$. We give a similar formula in the $sl_3$ case. |
1407.4772 | Alexander Ochirov Dr. | Henrik Johansson and Alexander Ochirov | Pure Gravities via Color-Kinematics Duality for Fundamental Matter | 48 pages + refs, 15 figures, 3 tables; v2 minor corrections, journal
version | JHEP 1511 (2015) 046 | 10.1007/JHEP11(2015)046 | CERN-PH-TH/2014-125, IPhT-t14/090 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We give a prescription for the computation of loop-level scattering
amplitudes in pure Einstein gravity, and four-dimensional pure supergravities,
using the color-kinematics duality. Amplitudes are constructed using double
copies of pure (super-)Yang-Mills parts and additional contributions from
double copies of fundamental matter, which are treated as ghosts. The
opposite-statistics states cancel the unwanted dilaton and axion in the bosonic
theory, as well as the extra matter supermultiplets in supergravities. As a
spinoff, we obtain a prescription for obtaining amplitudes in supergravities
with arbitrary non-self-interacting matter. As a prerequisite, we extend the
color-kinematics duality from the adjoint to the fundamental representation of
the gauge group. We explain the numerator relations that the fundamental
kinematic Lie algebra should satisfy. We give nontrivial evidence supporting
our construction using explicit tree and loop amplitudes, as well as more
general arguments.
| [
{
"created": "Thu, 17 Jul 2014 18:50:45 GMT",
"version": "v1"
},
{
"created": "Thu, 5 Nov 2015 12:43:35 GMT",
"version": "v2"
}
] | 2015-11-11 | [
[
"Johansson",
"Henrik",
""
],
[
"Ochirov",
"Alexander",
""
]
] | We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments. |
hep-th/0212289 | Dmitri Maximovitch Gitman | B. Geyer (U. of Leipzig), D.M. Gitman (U. of Sao Paulo), I.V. Tyutin
(Lebedev Institute) | Canonical form of Euler-Lagrange equations and gauge symmetries | 27 pages, LaTex file | J.Phys.A36:6587,2003 | 10.1088/0305-4470/36/23/321 | Publicacao IFUSP 1535/2002 | hep-th | null | The structure of the Euler-Lagrange equations for a general Lagrangian theory
is studied. For these equations we present a reduction procedure to the
so-called canonical form. In the canonical form the equations are solved with
respect to highest-order derivatives of nongauge coordinates, whereas gauge
coordinates and their derivatives enter in the right hand sides of the
equations as arbitrary functions of time. The reduction procedure reveals
constraints in the Lagrangian formulation of singular systems and, in that
respect, is similar to the Dirac procedure in the Hamiltonian formulation.
Moreover, the reduction procedure allows one to reveal the gauge identities
between the Euler-Lagrange equations. Thus, a constructive way of finding all
the gauge generators within the Lagrangian formulation is presented. At the
same time, it is proven that for local theories all the gauge generators are
local in time operators.
| [
{
"created": "Mon, 23 Dec 2002 17:47:15 GMT",
"version": "v1"
}
] | 2008-11-26 | [
[
"Geyer",
"B.",
"",
"U. of Leipzig"
],
[
"Gitman",
"D. M.",
"",
"U. of Sao Paulo"
],
[
"Tyutin",
"I. V.",
"",
"Lebedev Institute"
]
] | The structure of the Euler-Lagrange equations for a general Lagrangian theory is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter in the right hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proven that for local theories all the gauge generators are local in time operators. |
hep-th/9310065 | null | Aurelian Isar | Wigner distribution function for the harmonic oscillator with
dissipation within the theory of open quantum systems | 17 pages,plain TEX, FT-389-1993 | null | null | null | hep-th | null | Time evolution of the expectation values of various dynamical operators of
the harmonic oscillator with dissipation is analitically obtained within the
framework of the Lindblad's theory for open quantum systems. We deduce the
density matrix of the damped harmonic oscillator from the solution of the
Fokker-Planck equation for the coherent state representation, obtained from the
master equation for the density operator. The Fokker-Planck equation for the
Wigner distribution function is also solved by using the Wang-Uhlenbeck method
of transforming it into a linearized partial differential equation for the
Wigner function, subject to either the Gaussian type or the $\delta$-function
type of initial conditions. The Wigner functions which we obtain are
two-dimensional Gaussians with different widths.
| [
{
"created": "Tue, 12 Oct 1993 14:43:00 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Isar",
"Aurelian",
""
]
] | Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad's theory for open quantum systems. We deduce the density matrix of the damped harmonic oscillator from the solution of the Fokker-Planck equation for the coherent state representation, obtained from the master equation for the density operator. The Fokker-Planck equation for the Wigner distribution function is also solved by using the Wang-Uhlenbeck method of transforming it into a linearized partial differential equation for the Wigner function, subject to either the Gaussian type or the $\delta$-function type of initial conditions. The Wigner functions which we obtain are two-dimensional Gaussians with different widths. |
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