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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0908.0797
|
Ayan Mukhopadhyay
|
Ayan Mukhopadhyay
|
A Covariant Form of the Navier-Stokes Equation for the Galilean
Conformal Algebra
|
33 pages; accepted for publication in JHEP
|
JHEP 1001:100,2010
|
10.1007/JHEP01(2010)100
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We demonstrate that the Navier-Stokes equation can be covariantized under the
full infinite dimensional Galilean Conformal Algebra (GCA), such that it
reduces to the usual Navier-Stokes equation in an inertial frame. The
covariantization is possible only for incompressible flows, i.e when the
divergence of the velocity field vanishes. Using the continuity equation, we
can fix the transformation of pressure and density under GCA uniquely. We also
find that when all chemical potentials vanish, $c_{s}$, which denotes the speed
of sound in an inertial frame comoving with the flow, must either be a
fundamental constant or given in terms of microscopic parameters. We will
discuss how both could be possible. In absence of chemical potentials, we also
find that the covariance under GCA implies that either the viscosity should
vanish or the microscopic theory should have a length scale or a time scale or
both. We further find that the higher derivative corrections to the
Navier-Stokes equation, can be covariantized, only if they are restricted to
certain possible combinations in the inertial frame. We explicitly evaluate all
possible three derivative corrections. Finally, we argue that our analysis
hints that the parent relativistic theory with relativistic conformal symmetry
needs to be deformed before the contraction is taken to produce a sensible GCA
invariant dynamical limit.
|
[
{
"created": "Thu, 6 Aug 2009 05:35:22 GMT",
"version": "v1"
},
{
"created": "Mon, 14 Sep 2009 13:47:30 GMT",
"version": "v2"
},
{
"created": "Mon, 23 Nov 2009 05:35:57 GMT",
"version": "v3"
},
{
"created": "Tue, 29 Dec 2009 05:19:13 GMT",
"version": "v4"
}
] |
2014-11-20
|
[
[
"Mukhopadhyay",
"Ayan",
""
]
] |
We demonstrate that the Navier-Stokes equation can be covariantized under the full infinite dimensional Galilean Conformal Algebra (GCA), such that it reduces to the usual Navier-Stokes equation in an inertial frame. The covariantization is possible only for incompressible flows, i.e when the divergence of the velocity field vanishes. Using the continuity equation, we can fix the transformation of pressure and density under GCA uniquely. We also find that when all chemical potentials vanish, $c_{s}$, which denotes the speed of sound in an inertial frame comoving with the flow, must either be a fundamental constant or given in terms of microscopic parameters. We will discuss how both could be possible. In absence of chemical potentials, we also find that the covariance under GCA implies that either the viscosity should vanish or the microscopic theory should have a length scale or a time scale or both. We further find that the higher derivative corrections to the Navier-Stokes equation, can be covariantized, only if they are restricted to certain possible combinations in the inertial frame. We explicitly evaluate all possible three derivative corrections. Finally, we argue that our analysis hints that the parent relativistic theory with relativistic conformal symmetry needs to be deformed before the contraction is taken to produce a sensible GCA invariant dynamical limit.
|
hep-th/0312134
|
Arjan Keurentjes
|
Arjan Keurentjes
|
U-duality (sub-)groups and their topology
|
LaTeX, 8 pages, 2 tables, 1 figure, uses IOP-style files. Contributed
to the proceedings of the RTN-workshop ``The quantum structure of space-time
and the geometrical nature of the fundamental interactions,'', Copenhagen,
Denmark, september 2003
|
Class.Quant.Grav. 21 (2004) S1367-1374
|
10.1088/0264-9381/21/10/009
| null |
hep-th
| null |
We discuss some consequences of the fact that symmetry groups appearing in
compactified (super-)gravity may be non-simply connected. The possibility to
add fermions to a theory results in a simple criterion to decide whether a
3-dimensional coset sigma model can be interpreted as a dimensional reduction
of a higher dimensional theory. Similar criteria exist for higher dimensional
sigma models, though less decisive. Careful examination of the topology of
symmetry groups rules out certain proposals for M-theory symmetries, which are
not ruled out at the level of the algebra's. We conclude with an observation on
the relation between the ``generalized holonomy'' proposal, and the actual
symmetry groups resulting from E_10 and E_11 conjectures.
|
[
{
"created": "Fri, 12 Dec 2003 12:29:30 GMT",
"version": "v1"
}
] |
2009-11-10
|
[
[
"Keurentjes",
"Arjan",
""
]
] |
We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional coset sigma model can be interpreted as a dimensional reduction of a higher dimensional theory. Similar criteria exist for higher dimensional sigma models, though less decisive. Careful examination of the topology of symmetry groups rules out certain proposals for M-theory symmetries, which are not ruled out at the level of the algebra's. We conclude with an observation on the relation between the ``generalized holonomy'' proposal, and the actual symmetry groups resulting from E_10 and E_11 conjectures.
|
hep-th/9807219
|
Antonio Lima Santos
|
A. Lima-Santos
|
Bethe Ansatze for 19-vertex Models
|
30 pages, Latex, references added, no signficant changes
|
J.Phys.A32:1819-1839,1999
|
10.1088/0305-4470/32/10/004
| null |
hep-th
| null |
The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the
supersymmetric osp(1|2) with periodic boundary conditions are studied. We find
the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz.
The approche is a suitable parametrization of their wavefunctions. We also
applied the Algebraic Bethe Ansatz in order to obtain the eigenvalues and
eigenvectors of the corresponding transfer matrices.
|
[
{
"created": "Wed, 29 Jul 1998 15:29:09 GMT",
"version": "v1"
},
{
"created": "Wed, 3 Feb 1999 15:50:34 GMT",
"version": "v2"
}
] |
2010-04-08
|
[
[
"Lima-Santos",
"A.",
""
]
] |
The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The approche is a suitable parametrization of their wavefunctions. We also applied the Algebraic Bethe Ansatz in order to obtain the eigenvalues and eigenvectors of the corresponding transfer matrices.
|
hep-th/0212189
|
Kholodenko Arkady L.
|
Arkady L. Kholodenko
|
"New" Veneziano amplitudes from "old" Fermat (hyper) surfaces
|
92 pages LaTex, some typos removed, discussion section is added along
with several additional latest references
|
Int.J.Mod.Phys. 19 (2004) 1665-1703
|
10.1142/S0217751X04018166
| null |
hep-th math-ph math.MP
| null |
The history of discovery of bosonic string theory is well documented. This
theory evolved as an attempt to find a multidimensional analogue of Euler's
beta function. Such an analogue had in fact been known in mathematics
literature at least in 1922 and was studied subsequently by mathematicians such
as Selberg, Weil and Deligne among others. The mathematical interpretation of
this multidimensional beta function is markedly different from that described
in physics literature. This paper aims to bridge the gap between the existing
treatments. Preserving all results of conformal field theories intact,
developed formalism employing topological, algebro-geometric, number-theoretic
and combinatorial metods is aimed to provide better understanding of the
Veneziano amplitudes and, thus, of string theories.
|
[
{
"created": "Mon, 16 Dec 2002 22:14:55 GMT",
"version": "v1"
},
{
"created": "Wed, 18 Dec 2002 17:33:59 GMT",
"version": "v2"
},
{
"created": "Thu, 15 May 2003 22:21:25 GMT",
"version": "v3"
}
] |
2009-11-07
|
[
[
"Kholodenko",
"Arkady L.",
""
]
] |
The history of discovery of bosonic string theory is well documented. This theory evolved as an attempt to find a multidimensional analogue of Euler's beta function. Such an analogue had in fact been known in mathematics literature at least in 1922 and was studied subsequently by mathematicians such as Selberg, Weil and Deligne among others. The mathematical interpretation of this multidimensional beta function is markedly different from that described in physics literature. This paper aims to bridge the gap between the existing treatments. Preserving all results of conformal field theories intact, developed formalism employing topological, algebro-geometric, number-theoretic and combinatorial metods is aimed to provide better understanding of the Veneziano amplitudes and, thus, of string theories.
|
1406.6574
|
Jan Plefka
|
Johannes Broedel, Marius de Leeuw, Jan Plefka, Matteo Rosso
|
Constraining subleading soft gluon and graviton theorems
|
17 pages. v2: Two references fixed, half sentence after eq. (13)
added. v3: Terms in eq. (48) for S2G corrected
|
Phys. Rev. D 90, 065024 (2014)
|
10.1103/PhysRevD.90.065024
|
HU-EP-14/20
|
hep-th hep-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We show that the form of the recently proposed subleading soft graviton and
gluon theorems in any dimension are severely constrained by elementary
arguments based on Poincar\'e and gauge invariance as well as a
self-consistency condition arising from the distributional nature of scattering
amplitudes. Combined with the assumption of a local form as it would arise from
a Ward identity the orbital part of the subleading operators is completely
fixed by the leading universal Weinberg soft pole behavior. The polarization
part of the differential subleading soft operators in turn is determined up to
a single numerical factor for each hard leg at every order in the soft momentum
expansion. In four dimensions, factorization of the Lorentz group allows to fix
the subleading operators completely.
|
[
{
"created": "Wed, 25 Jun 2014 14:04:39 GMT",
"version": "v1"
},
{
"created": "Mon, 30 Jun 2014 12:46:16 GMT",
"version": "v2"
},
{
"created": "Fri, 4 Jul 2014 14:15:35 GMT",
"version": "v3"
}
] |
2014-09-24
|
[
[
"Broedel",
"Johannes",
""
],
[
"de Leeuw",
"Marius",
""
],
[
"Plefka",
"Jan",
""
],
[
"Rosso",
"Matteo",
""
]
] |
We show that the form of the recently proposed subleading soft graviton and gluon theorems in any dimension are severely constrained by elementary arguments based on Poincar\'e and gauge invariance as well as a self-consistency condition arising from the distributional nature of scattering amplitudes. Combined with the assumption of a local form as it would arise from a Ward identity the orbital part of the subleading operators is completely fixed by the leading universal Weinberg soft pole behavior. The polarization part of the differential subleading soft operators in turn is determined up to a single numerical factor for each hard leg at every order in the soft momentum expansion. In four dimensions, factorization of the Lorentz group allows to fix the subleading operators completely.
|
2102.07776
|
Murad Alim
|
Murad Alim
|
Intrinsic non-perturbative topological strings
|
35 pages, fixed an error in Prop. 4.2, added a remark on a previous
different analytic continuation of the resolved conifold free energies in Rem
4.7 and fixed several typos
| null | null | null |
hep-th math-ph math.AG math.MP
|
http://creativecommons.org/licenses/by/4.0/
|
We study difference equations which are obtained from the asymptotic
expansion of topological string theory on the deformed and the resolved
conifold geometries as well as for topological string theory on arbitrary
families of Calabi-Yau manifolds near generic singularities at finite distance
in the moduli space. Analytic solutions in the topological string coupling to
these equations are found. The solutions are given by known special functions
and can be used to extract the strong coupling expansion as well as the
non-perturbative content. The strong coupling expansions show the
characteristics of D-brane and NS5-brane contributions, this is illustrated for
the quintic Calabi-Yau threefold. For the resolved conifold, an expression
involving both the Gopakumar-Vafa resummation as well as the refined
topological string in the Nekrasov-Shatashvili limit is obtained and compared
to expected results in the literature. Furthermore, a precise relation between
the non-perturbative partition function of topological strings and the
generating function of non-commutative Donaldson-Thomas invariants is given.
Moreover, the expansion of the topological string on the resolved conifold near
its singular small volume locus is studied. Exact expressions for the leading
singular term as well as the regular terms in this expansion are provided and
proved. The constant term of this expansion turns out to be the known
Gromov-Witten constant map contribution.
|
[
{
"created": "Mon, 15 Feb 2021 19:00:00 GMT",
"version": "v1"
},
{
"created": "Fri, 16 Apr 2021 15:00:37 GMT",
"version": "v2"
}
] |
2021-04-19
|
[
[
"Alim",
"Murad",
""
]
] |
We study difference equations which are obtained from the asymptotic expansion of topological string theory on the deformed and the resolved conifold geometries as well as for topological string theory on arbitrary families of Calabi-Yau manifolds near generic singularities at finite distance in the moduli space. Analytic solutions in the topological string coupling to these equations are found. The solutions are given by known special functions and can be used to extract the strong coupling expansion as well as the non-perturbative content. The strong coupling expansions show the characteristics of D-brane and NS5-brane contributions, this is illustrated for the quintic Calabi-Yau threefold. For the resolved conifold, an expression involving both the Gopakumar-Vafa resummation as well as the refined topological string in the Nekrasov-Shatashvili limit is obtained and compared to expected results in the literature. Furthermore, a precise relation between the non-perturbative partition function of topological strings and the generating function of non-commutative Donaldson-Thomas invariants is given. Moreover, the expansion of the topological string on the resolved conifold near its singular small volume locus is studied. Exact expressions for the leading singular term as well as the regular terms in this expansion are provided and proved. The constant term of this expansion turns out to be the known Gromov-Witten constant map contribution.
|
hep-th/0402117
|
Jerzy Lukierski
|
Jerzy Lukierski (Inst. Theor. Phys. Wroclaw University)
|
Relation between quantum $\kappa$-Poincar\'{e} framework and Doubly
Special Relativity
|
12 pages, LaTeX style changed.Text file not changed. The paper will
appear in the Proceedings of the International Workshop "Supersymmetries and
Quantum Symmetries" (SQS'03 July 2003), Dubna 2004, Eds. E. Ivanov, A.
Pashnev
| null | null | null |
hep-th
| null |
We describe firstly the basic features of quantum $\kappa$-Poincar\'{e}
symmetries with their Hopf algebra structure. The quantum $\kappa$-Poincar\'{e}
framework in any basis relates rigidly the quantum $\kappa$-Poincar\'{e}
algebra with quantum $\kappa$-Poincar\'{e} group, noncommutative space-time and
$\kappa$-deformed phase space. Further we present the approach of Doubly
Special Relativity (DSR) theories, which introduce(in the version DSR1)
kinematically the frame - independent fundamental mass parameter as described
by maximal three-momentum $|\overrightarrow{p}|=\kappa c$. We argue why the DSR
theories in one-particle sector can be treated as the part of quantum
$\kappa$-Poincar\'{e} framework. The DSR formulation has been extended to
multiparticle states either in a way leading to nonlinear description of
classical relativistic symmetries, or providing the identification of DSR
approach with full quantum $\kappa$-Poincar\'{e} framework.
|
[
{
"created": "Mon, 16 Feb 2004 12:50:06 GMT",
"version": "v1"
},
{
"created": "Wed, 18 Feb 2004 09:03:05 GMT",
"version": "v2"
}
] |
2007-05-23
|
[
[
"Lukierski",
"Jerzy",
"",
"Inst. Theor. Phys. Wroclaw University"
]
] |
We describe firstly the basic features of quantum $\kappa$-Poincar\'{e} symmetries with their Hopf algebra structure. The quantum $\kappa$-Poincar\'{e} framework in any basis relates rigidly the quantum $\kappa$-Poincar\'{e} algebra with quantum $\kappa$-Poincar\'{e} group, noncommutative space-time and $\kappa$-deformed phase space. Further we present the approach of Doubly Special Relativity (DSR) theories, which introduce(in the version DSR1) kinematically the frame - independent fundamental mass parameter as described by maximal three-momentum $|\overrightarrow{p}|=\kappa c$. We argue why the DSR theories in one-particle sector can be treated as the part of quantum $\kappa$-Poincar\'{e} framework. The DSR formulation has been extended to multiparticle states either in a way leading to nonlinear description of classical relativistic symmetries, or providing the identification of DSR approach with full quantum $\kappa$-Poincar\'{e} framework.
|
hep-th/9605071
|
N. A. Papadopoulos
|
H. M. Bosselmann, N.A. Papadopoulos
|
TG-Equivariance of Connections and Gauge Transformations
|
12 pages
| null | null | null |
hep-th
| null |
We consider the notion of a connection on a principal bundle $P(M,G)$ from
the point of view of the action of the tangential group $TG$. This leads to a
new definition of a connection and allows to interpret gauge transformations as
effect of the $TG$ action.
|
[
{
"created": "Thu, 9 May 1996 18:44:42 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Bosselmann",
"H. M.",
""
],
[
"Papadopoulos",
"N. A.",
""
]
] |
We consider the notion of a connection on a principal bundle $P(M,G)$ from the point of view of the action of the tangential group $TG$. This leads to a new definition of a connection and allows to interpret gauge transformations as effect of the $TG$ action.
|
1302.2939
|
Christopher Ford
|
Bobby Cheng and Chris Ford
|
Fermion Zero Modes for Abelian BPS Monopoles
|
6 pages, 1 figure
| null |
10.1016/j.physletb.2013.02.022
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Fermion zero modes for abelian BPS monopoles are considered. In the
spherically symmetric case the normalisable zero modes are determined for
arbitrary monopole charge N. If N>1 the zero modes are zero along $N-1$
half-lines emanating from the monopole.
|
[
{
"created": "Tue, 12 Feb 2013 22:23:25 GMT",
"version": "v1"
}
] |
2015-06-15
|
[
[
"Cheng",
"Bobby",
""
],
[
"Ford",
"Chris",
""
]
] |
Fermion zero modes for abelian BPS monopoles are considered. In the spherically symmetric case the normalisable zero modes are determined for arbitrary monopole charge N. If N>1 the zero modes are zero along $N-1$ half-lines emanating from the monopole.
|
1107.2917
|
Diego Hofman
|
Diego M. Hofman and Andrew Strominger
|
Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
|
6 pages, no figures. v2: reference added, minor typos corrected
| null |
10.1103/PhysRevLett.107.161601
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
It is well known that a local, unitary Poincare-invariant 2D QFT with a
global scaling symmetry and a discrete non-negative spectrum of scaling
dimensions necessarily has both a left and a right local conformal symmetry. In
this paper we consider a chiral situation beginning with only a left global
scaling symmetry and do not assume Lorentz invariance. We find that a left
conformal symmetry is still implied, while right translations are enhanced
either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.
|
[
{
"created": "Thu, 14 Jul 2011 20:00:01 GMT",
"version": "v1"
},
{
"created": "Wed, 7 Sep 2011 15:21:45 GMT",
"version": "v2"
}
] |
2013-05-29
|
[
[
"Hofman",
"Diego M.",
""
],
[
"Strominger",
"Andrew",
""
]
] |
It is well known that a local, unitary Poincare-invariant 2D QFT with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this paper we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left conformal symmetry is still implied, while right translations are enhanced either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.
|
hep-th/0610106
|
Qing-Guo Huang
|
Qing-Guo Huang
|
Weak Gravity Conjecture with Large Extra Dimensions
|
8 pages; Refs added, version for publication in PLB
|
Phys.Lett.B658:155-157,2008
|
10.1016/j.physletb.2007.03.051
| null |
hep-th hep-ph
| null |
In the presence of large extra dimensions, the fundamental Planck scale can
be much lower than the apparent four-dimensional Planck scale. In this setup,
the weak gravity conjecture implies a much more stringent constraint on the UV
cutoff for the U(1) gauge theory in four dimensions. This new energy scale may
be relevant to LHC.
|
[
{
"created": "Tue, 10 Oct 2006 00:54:50 GMT",
"version": "v1"
},
{
"created": "Fri, 30 Mar 2007 01:31:01 GMT",
"version": "v2"
}
] |
2008-11-26
|
[
[
"Huang",
"Qing-Guo",
""
]
] |
In the presence of large extra dimensions, the fundamental Planck scale can be much lower than the apparent four-dimensional Planck scale. In this setup, the weak gravity conjecture implies a much more stringent constraint on the UV cutoff for the U(1) gauge theory in four dimensions. This new energy scale may be relevant to LHC.
|
1111.7293
|
Olaf Hohm
|
Olaf Hohm and Seung Ki Kwak
|
N=1 Supersymmetric Double Field Theory
|
22 pages, v2: minor corrections, ref. added, to appear in JHEP
| null |
10.1007/JHEP03(2012)080
|
MIT-CTP-4328; LMU-ASC 74/11
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We construct the N=1 supersymmetric extension of double field theory for
D=10, including the coupling to an arbitrary number n of abelian vector
multiplets. This theory features a local O(1,9+n) x O(1,9) tangent space
symmetry under which the fermions transform. It is shown that the supersymmetry
transformations close into the generalized diffeomorphisms of double field
theory.
|
[
{
"created": "Wed, 30 Nov 2011 20:03:13 GMT",
"version": "v1"
},
{
"created": "Fri, 23 Mar 2012 11:03:57 GMT",
"version": "v2"
}
] |
2015-06-03
|
[
[
"Hohm",
"Olaf",
""
],
[
"Kwak",
"Seung Ki",
""
]
] |
We construct the N=1 supersymmetric extension of double field theory for D=10, including the coupling to an arbitrary number n of abelian vector multiplets. This theory features a local O(1,9+n) x O(1,9) tangent space symmetry under which the fermions transform. It is shown that the supersymmetry transformations close into the generalized diffeomorphisms of double field theory.
|
hep-th/9408119
|
Terry Gannon
|
Terry Gannon
|
The Classification of SU(m)_{k} Automorphism Invariants
|
8 pp. (plain tex)
| null | null | null |
hep-th
| null |
In this paper we find all permutations of the level k weights of the affine
algebra A_r^{(1)} which commute with both its S and T modular matrices. We find
that all of these are simple current automorphisms and their conjugations.
Previously, the A_{r,k}^{(1)} automorphism invariants were known only for r=1,2
\forall k, and k=1 \forall r. This is a major step toward the full
classification of all A_{r,k}^{(1)} modular invariants; the simplicity of this
proof strongly suggests that the full classification should be accomplishable.
In an appendix we collect some new results concerning the A_{r,k}^{(1)} fusion
ring.
|
[
{
"created": "Mon, 22 Aug 1994 13:40:50 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Gannon",
"Terry",
""
]
] |
In this paper we find all permutations of the level k weights of the affine algebra A_r^{(1)} which commute with both its S and T modular matrices. We find that all of these are simple current automorphisms and their conjugations. Previously, the A_{r,k}^{(1)} automorphism invariants were known only for r=1,2 \forall k, and k=1 \forall r. This is a major step toward the full classification of all A_{r,k}^{(1)} modular invariants; the simplicity of this proof strongly suggests that the full classification should be accomplishable. In an appendix we collect some new results concerning the A_{r,k}^{(1)} fusion ring.
|
2007.00034
|
Eftychia Sagkrioti
|
Eftychia Sagkrioti
|
A generalized method for all-loop results in $\lambda$-models
|
29 pages
| null |
10.1007/JHEP08(2020)050
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We compute the anomalous dimension of the single current operator in the case
of single and doubly deformed asymmetric $\lambda$-models with a general
deformation matrix. Our method uses the underlying geometry of the coupling
space, as well as an auxiliary group interaction, which completely decouples
from the asymmetric model in a specific limit, consistent with the
Renormalization Group flow. Our results are valid to all orders in the
deformation parameters and leading order to the levels of the underlying
current algebras. We specialize our general result to several models of
particular interest that have been constructed in the literature and for which
these anomalous dimensions were not known.
|
[
{
"created": "Tue, 30 Jun 2020 18:04:23 GMT",
"version": "v1"
}
] |
2020-08-26
|
[
[
"Sagkrioti",
"Eftychia",
""
]
] |
We compute the anomalous dimension of the single current operator in the case of single and doubly deformed asymmetric $\lambda$-models with a general deformation matrix. Our method uses the underlying geometry of the coupling space, as well as an auxiliary group interaction, which completely decouples from the asymmetric model in a specific limit, consistent with the Renormalization Group flow. Our results are valid to all orders in the deformation parameters and leading order to the levels of the underlying current algebras. We specialize our general result to several models of particular interest that have been constructed in the literature and for which these anomalous dimensions were not known.
|
hep-th/0407130
|
Sandip P. Trivedi
|
Lars Goerlich, Shamit Kachru, Prasanta K. Tripathy and Sandip P.
Trivedi
|
Gaugino Condensation and Nonperturbative Superpotentials in Flux
Compactifications
|
24 pages, harvmac, no figures, references added
|
JHEP 0412:074,2004
|
10.1088/1126-6708/2004/12/074
|
SU-ITP-04, SLAC-PUB-10502,TIFR/TH/04-17
|
hep-th
| null |
There are two known sources of nonperturbative superpotentials for K\"ahler
moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau
fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7
brane gauge theories. The first class of effects, Euclidean D3 branes which
lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the
fourfold, is relatively well understood. The second class has been less
explored. In this paper, we consider the explicit example of F-theory on $K3
\times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize
stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories
exhibit gaugino condensation, and generate a nonperturbative superpotential for
K\"ahler moduli. We describe how the relevant geometries in general contain
cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can
contribute to the superpotential, in the presence of flux). This second class
of effects is likely to be important in finding even larger classes of models
where the KKLT mechanism of moduli stabilization can be realized. We also
address various claims about the situation for IIB models with a single
K\"ahler modulus.
|
[
{
"created": "Thu, 15 Jul 2004 06:30:22 GMT",
"version": "v1"
},
{
"created": "Fri, 20 Aug 2004 10:13:46 GMT",
"version": "v2"
}
] |
2009-11-10
|
[
[
"Goerlich",
"Lars",
""
],
[
"Kachru",
"Shamit",
""
],
[
"Tripathy",
"Prasanta K.",
""
],
[
"Trivedi",
"Sandip P.",
""
]
] |
There are two known sources of nonperturbative superpotentials for K\"ahler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for K\"ahler moduli. We describe how the relevant geometries in general contain cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can contribute to the superpotential, in the presence of flux). This second class of effects is likely to be important in finding even larger classes of models where the KKLT mechanism of moduli stabilization can be realized. We also address various claims about the situation for IIB models with a single K\"ahler modulus.
|
hep-th/0007058
|
Emery Sokatchev
|
Sergio Ferrara and Emery Sokatchev
|
Conformal superfields and BPS states in AdS_4/7 geometries
|
To appear in the proceedings of the Euroconference ``Noncommutative
geometry and Hopf algebras in field theory and particle physics", Torino,
Villa Gualino (Italy), September 20-30, 1999
|
Int.J.Mod.Phys. B14 (2000) 2315
|
10.1142/S0217979200001837
| null |
hep-th
| null |
We carry out a general analysis of the representations of the superconformal
algebras OSp(8/4,R) and OSp(8*/2N) in terms of harmonic superspace. We present
a construction of their highest-weight UIR's by multiplication of the different
types of massless conformal superfields ("supersingletons"). Particular
attention is paid to the so-called "short multiplets". Representations
undergoing shortening have "protected dimension" and may correspond to BPS
states in the dual supergravity theory in anti-de Sitter space. These results
are relevant for the classification of multitrace operators in boundary
conformally invariant theories as well as for the classification of AdS black
holes preserving different fractions of supersymmetry.
|
[
{
"created": "Fri, 7 Jul 2000 10:16:20 GMT",
"version": "v1"
}
] |
2009-10-31
|
[
[
"Ferrara",
"Sergio",
""
],
[
"Sokatchev",
"Emery",
""
]
] |
We carry out a general analysis of the representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.
|
hep-th/0304117
|
Max Niedermaier
|
M. Niedermaier
|
Dimensionally reduced gravity theories are asymptotically safe
|
47 pages, Latex, 1 figure
|
Nucl.Phys. B673 (2003) 131-169
|
10.1016/j.nuclphysb.2003.09.015
| null |
hep-th gr-qc
| null |
4D Einstein gravity coupled to scalars and abelian gauge fields in its
2-Killing vector reduction is shown to be quasi-renormalizable to all loop
orders at the expense of introducing infinitely many essential couplings. The
latter can be combined into one or two functions of the `area radius'
associated with the two Killing vectors. The renormalization flow of these
couplings is governed by beta functionals expressible in closed form in terms
of the (one coupling) beta function of a symmetric space sigma-model.
Generically the matter coupled systems are asymptotically safe, that is the
flow possesses a non-trivial UV stable fixed point at which the trace anomaly
vanishes. The main exception is a minimal coupling of 4D Einstein gravity to
massless free scalars, in which case the scalars decouple from gravity at the
fixed point.
|
[
{
"created": "Fri, 11 Apr 2003 22:27:48 GMT",
"version": "v1"
}
] |
2015-06-26
|
[
[
"Niedermaier",
"M.",
""
]
] |
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the `area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow possesses a non-trivial UV stable fixed point at which the trace anomaly vanishes. The main exception is a minimal coupling of 4D Einstein gravity to massless free scalars, in which case the scalars decouple from gravity at the fixed point.
|
hep-th/0406171
|
Beatriz de Carlos
|
B. de Carlos, J. Roberts, Y. Schmohe
|
Moving Five-Branes and Membrane Instantons in Low Energy Heterotic
M-Theory
|
19 pages, 7 figures; revtex4
|
Phys.Rev. D71 (2005) 026004
|
10.1103/PhysRevD.71.026004
|
CERN-PH-TH/2004-106
|
hep-th hep-ph
| null |
We study cosmological solutions in the context of 4-dimensional low energy
Heterotic M-theory with moving bulk branes. In particular we present
non-trivial, analytic axion solutions generated by new symmetries of the full
potential-free action which are similar to 'triple axion' solutions found in
Pre-Big-Bang (PBB) cosmologies. We also consider the presence of a
non-perturbative superpotential, for which we find cosmological solutions with
and without a background perfect fluid. In the absence of a fluid the dilaton
and the T-modulus go to the potential-free solutions at late time, while the
moving brane tries to avoid colliding with the boundary and stabilize within
the bulk. When the fluid is included, we find that the real parts of the fields
track its behaviour and that the moving brane gets stabilized at the middle
point between the boundaries. In this latter case we can make analytic
approximations for the evolution of the fields whether or not axions are
included and we consider the possibility of this set up being a realization of
the quintessential scenario.
|
[
{
"created": "Mon, 21 Jun 2004 08:19:52 GMT",
"version": "v1"
}
] |
2009-11-10
|
[
[
"de Carlos",
"B.",
""
],
[
"Roberts",
"J.",
""
],
[
"Schmohe",
"Y.",
""
]
] |
We study cosmological solutions in the context of 4-dimensional low energy Heterotic M-theory with moving bulk branes. In particular we present non-trivial, analytic axion solutions generated by new symmetries of the full potential-free action which are similar to 'triple axion' solutions found in Pre-Big-Bang (PBB) cosmologies. We also consider the presence of a non-perturbative superpotential, for which we find cosmological solutions with and without a background perfect fluid. In the absence of a fluid the dilaton and the T-modulus go to the potential-free solutions at late time, while the moving brane tries to avoid colliding with the boundary and stabilize within the bulk. When the fluid is included, we find that the real parts of the fields track its behaviour and that the moving brane gets stabilized at the middle point between the boundaries. In this latter case we can make analytic approximations for the evolution of the fields whether or not axions are included and we consider the possibility of this set up being a realization of the quintessential scenario.
|
hep-th/0010289
|
Troost Jan
|
Victor Kac and Jan Troost
|
The stability of vacua in two-dimensional gauge theory
|
12 pages, 1 figure
|
Phys.Lett. B501 (2001) 313-318
|
10.1016/S0370-2693(01)00163-0
|
MIT-CTP 3039
|
hep-th
| null |
We discuss the stability of vacua in two-dimensional gauge theory for any
simple, simply connected gauge group. Making use of the representation of a
vacuum in terms of a Wilson line at infinity, we determine which vacua are
stable against pair production of heavy matter in the adjoint of the gauge
group. By calculating correlators of Wilson loops, we reduce the problem to a
problem in representation theory of Lie groups, that we solve in full
generality.
|
[
{
"created": "Tue, 31 Oct 2000 14:38:44 GMT",
"version": "v1"
}
] |
2009-10-31
|
[
[
"Kac",
"Victor",
""
],
[
"Troost",
"Jan",
""
]
] |
We discuss the stability of vacua in two-dimensional gauge theory for any simple, simply connected gauge group. Making use of the representation of a vacuum in terms of a Wilson line at infinity, we determine which vacua are stable against pair production of heavy matter in the adjoint of the gauge group. By calculating correlators of Wilson loops, we reduce the problem to a problem in representation theory of Lie groups, that we solve in full generality.
|
1012.3014
|
Norman Rink
|
Nicholas S. Manton, Norman A. Rink
|
Geometry and Energy of Non-abelian Vortices
|
22 pages, 1 figure
|
J. Math. Phys. 52, 043511 (2011)
|
10.1063/1.3574357
|
DAMTP-2010-117
|
hep-th math-ph math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study pure Yang--Mills theory on $\Sigma\times S^2$, where $\Sigma$ is a
compact Riemann surface, and invariance is assumed under rotations of $S^2$. It
is well known that the self-duality equations in this set-up reduce to vortex
equations on $\Sigma$. If the Yang--Mills gauge group is $\SU{2}$, the
Bogomolny vortex equations of the abelian Higgs model are obtained. For larger
gauge groups one generally finds vortex equations involving several
matrix-valued Higgs fields. Here we focus on Yang--Mills theory with gauge
group $\SU{N}/\ZZ_N$ and a special reduction which yields only one non-abelian
Higgs field. One of the new features of this reduction is the fact that while
the instanton number of the theory in four dimensions is generally fractional
with denominator $N$, we still obtain an integral vortex number in the reduced
theory. We clarify the relation between these two topological charges at a
bundle geometric level. Another striking feature is the emergence of
non-trivial lower and upper bounds for the energy of the reduced theory on
$\Sigma$. These bounds are proportional to the area of $\Sigma$. We give
special solutions of the theory on $\Sigma$ by embedding solutions of the
abelian Higgs model into the non-abelian theory, and we relate our work to the
language of quiver bundles, which has recently proved fruitful in the study of
dimensional reduction of Yang--Mills theory.
|
[
{
"created": "Tue, 14 Dec 2010 13:03:13 GMT",
"version": "v1"
}
] |
2011-05-02
|
[
[
"Manton",
"Nicholas S.",
""
],
[
"Rink",
"Norman A.",
""
]
] |
We study pure Yang--Mills theory on $\Sigma\times S^2$, where $\Sigma$ is a compact Riemann surface, and invariance is assumed under rotations of $S^2$. It is well known that the self-duality equations in this set-up reduce to vortex equations on $\Sigma$. If the Yang--Mills gauge group is $\SU{2}$, the Bogomolny vortex equations of the abelian Higgs model are obtained. For larger gauge groups one generally finds vortex equations involving several matrix-valued Higgs fields. Here we focus on Yang--Mills theory with gauge group $\SU{N}/\ZZ_N$ and a special reduction which yields only one non-abelian Higgs field. One of the new features of this reduction is the fact that while the instanton number of the theory in four dimensions is generally fractional with denominator $N$, we still obtain an integral vortex number in the reduced theory. We clarify the relation between these two topological charges at a bundle geometric level. Another striking feature is the emergence of non-trivial lower and upper bounds for the energy of the reduced theory on $\Sigma$. These bounds are proportional to the area of $\Sigma$. We give special solutions of the theory on $\Sigma$ by embedding solutions of the abelian Higgs model into the non-abelian theory, and we relate our work to the language of quiver bundles, which has recently proved fruitful in the study of dimensional reduction of Yang--Mills theory.
|
1309.6574
|
David A. Lowe
|
David A. Lowe, Ilies Messamah, Antun Skanata
|
Hidden Kerr/CFT at finite frequencies
|
23 pages, 6 figures, v2 some typos fixed and references added
|
Phys. Rev. D 89, 064005 (2014)
|
10.1103/PhysRevD.89.064005
|
BROWN-HET-1646
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Massless fields propagating in a generic Kerr black hole background enjoy a
hidden SL(2,R)xSL(2,R) symmetry. We determine how the exact mode functions
decompose into representations of this symmetry group. This extends earlier
results on the low frequency limit of the massless scalar case to finite
frequencies and general spin. As an application, we numerically determine the
parameters of the representations that appear in quasinormal modes. These
results represent a first step to formulating a more precise mapping to a
holographic dual conformal field theory for generic black holes.
|
[
{
"created": "Wed, 25 Sep 2013 17:03:43 GMT",
"version": "v1"
},
{
"created": "Tue, 29 Oct 2013 00:02:40 GMT",
"version": "v2"
}
] |
2014-03-12
|
[
[
"Lowe",
"David A.",
""
],
[
"Messamah",
"Ilies",
""
],
[
"Skanata",
"Antun",
""
]
] |
Massless fields propagating in a generic Kerr black hole background enjoy a hidden SL(2,R)xSL(2,R) symmetry. We determine how the exact mode functions decompose into representations of this symmetry group. This extends earlier results on the low frequency limit of the massless scalar case to finite frequencies and general spin. As an application, we numerically determine the parameters of the representations that appear in quasinormal modes. These results represent a first step to formulating a more precise mapping to a holographic dual conformal field theory for generic black holes.
|
1703.00455
|
Arnav Tripathy
|
Shamit Kachru and Arnav Tripathy
|
BPS jumping loci and special cycles
|
24 pages. Comments welcome!
| null | null | null |
hep-th math.AG
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study BPS jumping loci, or the subloci in moduli spaces of supersymmetric
string vacua where BPS states come into existence discontinuously. This
phenomenon is distinct from wall-crossing. We argue that these loci should be
thought of as special cycles in the sense of Noether-Lefschetz loci or special
Shimura subvarieties, which are indeed examples of BPS jumping loci for certain
string compactifications. We use the Hodge-elliptic genus as an informative
tool, suggesting that our work can be extended to understand the jumping
behavior of motivic Donaldson-Thomas invariants.
|
[
{
"created": "Wed, 1 Mar 2017 19:00:03 GMT",
"version": "v1"
},
{
"created": "Fri, 30 Jun 2017 22:14:00 GMT",
"version": "v2"
}
] |
2017-07-04
|
[
[
"Kachru",
"Shamit",
""
],
[
"Tripathy",
"Arnav",
""
]
] |
We study BPS jumping loci, or the subloci in moduli spaces of supersymmetric string vacua where BPS states come into existence discontinuously. This phenomenon is distinct from wall-crossing. We argue that these loci should be thought of as special cycles in the sense of Noether-Lefschetz loci or special Shimura subvarieties, which are indeed examples of BPS jumping loci for certain string compactifications. We use the Hodge-elliptic genus as an informative tool, suggesting that our work can be extended to understand the jumping behavior of motivic Donaldson-Thomas invariants.
|
hep-th/9702062
|
Naohisa Ogawa
|
Naohisa Ogawa
|
Pedagogical Introduction to Hamiltonian BRST formalism
|
8 pages, No figures, Latex, One small mistake of equation has been
repaired from the first version
| null | null |
SAKKYO-9702001
|
hep-th
| null |
Hamiltonian BRST formalism (FV formalism) includes many auxiliary fields
without explanation. Its path-integration has a simple form by using BRST
charge, but its construction is quite mechanically and hard to understand
physical meaning. In this paper we perform the phase space path-integral with
requiring BRST invariance for action and measure, and show that the resultant
form is equivalent to the Hamiltonian BRST (FV) formalism in gravitational
theory. This explains why so many auxiliary fields are necessary to be
introduced. We also find the gauge fixing is automatically done by requiring
the BRST invariance of the path-integral measure. This is a pedagogical
introduction to Hamiltonian BRST formalism.
|
[
{
"created": "Fri, 7 Feb 1997 12:49:30 GMT",
"version": "v1"
},
{
"created": "Wed, 12 Feb 1997 16:55:21 GMT",
"version": "v2"
}
] |
2008-02-03
|
[
[
"Ogawa",
"Naohisa",
""
]
] |
Hamiltonian BRST formalism (FV formalism) includes many auxiliary fields without explanation. Its path-integration has a simple form by using BRST charge, but its construction is quite mechanically and hard to understand physical meaning. In this paper we perform the phase space path-integral with requiring BRST invariance for action and measure, and show that the resultant form is equivalent to the Hamiltonian BRST (FV) formalism in gravitational theory. This explains why so many auxiliary fields are necessary to be introduced. We also find the gauge fixing is automatically done by requiring the BRST invariance of the path-integral measure. This is a pedagogical introduction to Hamiltonian BRST formalism.
|
1602.01503
|
Yuji Tachikawa
|
Takahiro Nishinaka and Yuji Tachikawa
|
On 4d rank-one N=3 superconformal field theories
|
24 pages
| null |
10.1007/JHEP09(2016)116
|
IPMU-16-0009, UT-16-03, YITP-16-8
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study the properties of 4d N=3 superconformal field theories whose rank is
one, i.e. those that reduce to a single vector multiplet on their moduli space
of vacua. We find that the moduli space can only be of the form C^3/Z_k for
k=1,2,3,4,6, and that the supersymmetry automatically enhances to N=4 for
k=1,2. In addition, we determine the central charges a and c in terms of k, and
construct the associated 2d chiral algebras, which turn out to be exotic N=2
supersymmetric W-algebras.
|
[
{
"created": "Wed, 3 Feb 2016 22:41:21 GMT",
"version": "v1"
}
] |
2016-10-12
|
[
[
"Nishinaka",
"Takahiro",
""
],
[
"Tachikawa",
"Yuji",
""
]
] |
We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for k=1,2,3,4,6, and that the supersymmetry automatically enhances to N=4 for k=1,2. In addition, we determine the central charges a and c in terms of k, and construct the associated 2d chiral algebras, which turn out to be exotic N=2 supersymmetric W-algebras.
|
1405.7184
|
Diego Rubiera-Garcia
|
Gonzalo J. Olmo and D. Rubiera-Garcia
|
Brane-world and loop cosmology from a gravity-matter coupling
perspective
|
8 pages, revtex4-1 style
|
Phys. Lett. B 740 (2015) 73
|
10.1016/j.physletb.2014.11.034
|
IFIC/14-51
|
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We show that the effective brane-world and the loop quantum cosmology
background expansion histories can be reproduced from a modified gravity
perspective in terms of an $f(R)$ gravity action plus a $g(R)$ term
non-minimally coupled with the matter Lagrangian. The reconstruction algorithm
that we provide depends on a free function of the matter density that must be
specified in each case and allows to obtain analytical solutions always. In the
simplest cases, the function $f(R)$ is quadratic in the Ricci scalar, $R$,
whereas $g(R)$ is linear. Our approach is compared with recent results in the
literature. We show that working in the Palatini formalism there is no need to
impose any constraint that keeps the equations second-order, which is a key
requirement for the successful implementation of the reconstruction algorithm.
|
[
{
"created": "Wed, 28 May 2014 10:26:16 GMT",
"version": "v1"
}
] |
2015-12-09
|
[
[
"Olmo",
"Gonzalo J.",
""
],
[
"Rubiera-Garcia",
"D.",
""
]
] |
We show that the effective brane-world and the loop quantum cosmology background expansion histories can be reproduced from a modified gravity perspective in terms of an $f(R)$ gravity action plus a $g(R)$ term non-minimally coupled with the matter Lagrangian. The reconstruction algorithm that we provide depends on a free function of the matter density that must be specified in each case and allows to obtain analytical solutions always. In the simplest cases, the function $f(R)$ is quadratic in the Ricci scalar, $R$, whereas $g(R)$ is linear. Our approach is compared with recent results in the literature. We show that working in the Palatini formalism there is no need to impose any constraint that keeps the equations second-order, which is a key requirement for the successful implementation of the reconstruction algorithm.
|
1309.3144
|
Sunandan Gangopadhyay
|
Sunandan Gangopadhyay, Frederik G Scholtz
|
Path integral action of a particle in a magnetic field in the
noncommutative plane and the Aharonov-Bohm effect
|
12 pages Latex, References added, To appear in J.Phys.A
|
J. Phys. A: Math. Theor. 47 (2014) 075301
|
10.1088/1751-8113/47/7/075301
| null |
hep-th quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The formulation of noncommutative quantum mechanics as a quantum system
represented in the space of Hilbert-Schmidt operators is used to systematically
derive, using the standard time slicing procedure, the path integral action for
a particle moving in the noncommutative plane and in the presence of a magnetic
field and an arbitrary potential. Using this action, the equation of motion and
the ground state energy for the partcle are obtained explicitly. The
Aharonov-Bohm phase is derived using a variety of methods and several dualities
between this system and other commutative and noncommutative systems are
demonstrated. Finally, the equivalence of the path integral formulation with
the noncommutative Schr\"{o}dinger equation is also established.
|
[
{
"created": "Thu, 12 Sep 2013 12:59:40 GMT",
"version": "v1"
},
{
"created": "Wed, 8 Jan 2014 09:53:13 GMT",
"version": "v2"
}
] |
2014-02-11
|
[
[
"Gangopadhyay",
"Sunandan",
""
],
[
"Scholtz",
"Frederik G",
""
]
] |
The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a particle moving in the noncommutative plane and in the presence of a magnetic field and an arbitrary potential. Using this action, the equation of motion and the ground state energy for the partcle are obtained explicitly. The Aharonov-Bohm phase is derived using a variety of methods and several dualities between this system and other commutative and noncommutative systems are demonstrated. Finally, the equivalence of the path integral formulation with the noncommutative Schr\"{o}dinger equation is also established.
|
hep-th/9407053
| null |
Bo-Yu Hou (Northwest University, Xi'an China), Bo-Yuan Hou (Chinese
Academy of Sciences, Beijing, China), and Zhong-Qi Ma (Institute of High
Energy Physics, Beijing, China)
|
$q$-Deformed Chern Characters for Quantum Groups $SU_{q}(N)$
| null |
J.Math.Phys.36:5110-5138,1995
|
10.1063/1.531217
|
BIHEP-TH-94-20
|
hep-th math.QA
| null |
In this paper, we introduce an $N\times N$ matrix $\epsilon^{a\bar{b}}$ in
the quantum groups $SU_{q}(N)$ to transform the conjugate representation into
the standard form so that we are able to compute the explicit forms of the
important quantities in the bicovariant differential calculus on $SU_{q}(N)$,
such as the $q$-deformed structure constant ${\bf C}_{IJ}^{~K}$ and the
$q$-deformed transposition operator $\Lambda$. From the $q$-gauge covariant
condition we define the generalized $q$-deformed Killing form and the $m$-th
$q$-deformed Chern class $P_{m}$ for the quantum groups $SU_{q}(N)$. Some
useful relations of the generalized $q$-deformed Killing form are presented. In
terms of the $q$-deformed homotopy operator we are able to compute the
$q$-deformed Chern-Simons $Q_{2m-1}$ by the condition $dQ_{2m-1}=P_{m}$,
Furthermore, the $q$-deformed cocycle hierarchy, the $q$-deformed gauge
covariant Lagrangian, and the $q$-deformed Yang-Mills equation are derived.
|
[
{
"created": "Mon, 11 Jul 1994 20:06:15 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Hou",
"Bo-Yu",
"",
"Northwest University, Xi'an China"
],
[
"Hou",
"Bo-Yuan",
"",
"Chinese\n Academy of Sciences, Beijing, China"
],
[
"Ma",
"Zhong-Qi",
"",
"Institute of High\n Energy Physics, Beijing, China"
]
] |
In this paper, we introduce an $N\times N$ matrix $\epsilon^{a\bar{b}}$ in the quantum groups $SU_{q}(N)$ to transform the conjugate representation into the standard form so that we are able to compute the explicit forms of the important quantities in the bicovariant differential calculus on $SU_{q}(N)$, such as the $q$-deformed structure constant ${\bf C}_{IJ}^{~K}$ and the $q$-deformed transposition operator $\Lambda$. From the $q$-gauge covariant condition we define the generalized $q$-deformed Killing form and the $m$-th $q$-deformed Chern class $P_{m}$ for the quantum groups $SU_{q}(N)$. Some useful relations of the generalized $q$-deformed Killing form are presented. In terms of the $q$-deformed homotopy operator we are able to compute the $q$-deformed Chern-Simons $Q_{2m-1}$ by the condition $dQ_{2m-1}=P_{m}$, Furthermore, the $q$-deformed cocycle hierarchy, the $q$-deformed gauge covariant Lagrangian, and the $q$-deformed Yang-Mills equation are derived.
|
hep-th/0002145
|
Juan Maldacena
|
Stephen Hawking, Juan Maldacena and Andrew Strominger
|
DeSitter entropy, quantum entanglement and ADS/CFT
|
harvmac, 2 figures
|
JHEP 0105:001,2001
|
10.1088/1126-6708/2001/05/001
| null |
hep-th
| null |
A deSitter brane-world bounding regions of anti-deSitter space has a
macroscopic entropy given by one-quarter the area of the observer horizon. A
proposed variant of the AdS/CFT correspondence gives a dual description of this
cosmology as conformal field theory coupled to gravity in deSitter space. In
the case of two-dimensional deSitter space this provides a microscopic
derivation of the entropy, including the one-quarter, as quantum entanglement
of the conformal field theory across the horizon.
|
[
{
"created": "Thu, 17 Feb 2000 14:52:35 GMT",
"version": "v1"
}
] |
2009-10-31
|
[
[
"Hawking",
"Stephen",
""
],
[
"Maldacena",
"Juan",
""
],
[
"Strominger",
"Andrew",
""
]
] |
A deSitter brane-world bounding regions of anti-deSitter space has a macroscopic entropy given by one-quarter the area of the observer horizon. A proposed variant of the AdS/CFT correspondence gives a dual description of this cosmology as conformal field theory coupled to gravity in deSitter space. In the case of two-dimensional deSitter space this provides a microscopic derivation of the entropy, including the one-quarter, as quantum entanglement of the conformal field theory across the horizon.
|
hep-th/9605231
|
Billy D. Jones
|
Billy D. Jones (1), Robert J. Perry (1), Stanislaw D. Glazek (2) ((1)
The Ohio State University, (2) Warsaw University, Poland)
|
Analytic Treatment of Positronium Spin Splittings in Light-Front QED
|
46 pages, latex, 3 Postscript figures included, section on remaining
corrections added, title changed, error in older version corrected, cutoff
placed in a window
|
Phys.Rev. D55 (1997) 6561-6583
|
10.1103/PhysRevD.55.6561
| null |
hep-th hep-ph nucl-th
| null |
We study the QED bound-state problem in a light-front hamiltonian approach.
Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements
between free states of drastically different energies removed, we perform a
similarity transformation that removes the matrix elements between free states
with energy differences between the bare cutoff, $\Lambda$, and effective
cutoff, $\lam$ ($\lam < \Lam$). This generates effective interactions in the
renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived
to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized
by requiring it to satisfy coupling coherence. A nonrelativistic limit of the
theory is taken, and the resulting Hamiltonian is studied using bound-state
perturbation theory (BSPT). The effective cutoff, $\lam^2$, is fixed, and the
limit, $0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow
\infty$, is taken. This upper bound on $\lam^2$ places the effects of
low-energy (energy transfer below $\lam$) emission in the effective
interactions in the $| e {\overline e} > $ sector. This lower bound on $\lam^2$
insures that the nonperturbative scale of interest is not removed by the
similarity transformation. As an explicit example of the general formalism
introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces
the exact spectrum of spin splittings, with degeneracies dictated by rotational
symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is
performed analytically, and gives the well known singlet-triplet ground state
spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining
corrections other than the spin splittings and how they can be treated in
calculating the spectrum with higher precision.
|
[
{
"created": "Sat, 1 Jun 1996 12:22:45 GMT",
"version": "v1"
},
{
"created": "Fri, 12 Jul 1996 16:56:03 GMT",
"version": "v2"
},
{
"created": "Fri, 21 Feb 1997 21:59:52 GMT",
"version": "v3"
}
] |
2009-10-30
|
[
[
"Jones",
"Billy D.",
""
],
[
"Perry",
"Robert J.",
""
],
[
"Glazek",
"Stanislaw D.",
""
]
] |
We study the QED bound-state problem in a light-front hamiltonian approach. Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, $\Lambda$, and effective cutoff, $\lam$ ($\lam < \Lam$). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized by requiring it to satisfy coupling coherence. A nonrelativistic limit of the theory is taken, and the resulting Hamiltonian is studied using bound-state perturbation theory (BSPT). The effective cutoff, $\lam^2$, is fixed, and the limit, $0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow \infty$, is taken. This upper bound on $\lam^2$ places the effects of low-energy (energy transfer below $\lam$) emission in the effective interactions in the $| e {\overline e} > $ sector. This lower bound on $\lam^2$ insures that the nonperturbative scale of interest is not removed by the similarity transformation. As an explicit example of the general formalism introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces the exact spectrum of spin splittings, with degeneracies dictated by rotational symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is performed analytically, and gives the well known singlet-triplet ground state spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining corrections other than the spin splittings and how they can be treated in calculating the spectrum with higher precision.
|
hep-th/9711002
|
Sasha Polyakov
|
A. Polyakov
|
String Theory and Quark Confinement
|
13 pages, latex; talk at STRINGS'97
|
Nucl.Phys.Proc.Suppl. 68 (1998) 1-8
|
10.1016/S0920-5632(98)00135-2
|
PUPT-1743
|
hep-th
| null |
This article is based on a talk given at the ``Strings'97'' conference. It
discusses the search for the universality class of confining strings. The key
ingredients include the loop equations, the zigzag symmetry, the non-linear
renormalization group. Some new tests for the equivalence between gauge fields
and strings are proposed.
|
[
{
"created": "Sat, 1 Nov 1997 22:45:54 GMT",
"version": "v1"
}
] |
2009-10-30
|
[
[
"Polyakov",
"A.",
""
]
] |
This article is based on a talk given at the ``Strings'97'' conference. It discusses the search for the universality class of confining strings. The key ingredients include the loop equations, the zigzag symmetry, the non-linear renormalization group. Some new tests for the equivalence between gauge fields and strings are proposed.
|
hep-th/0701200
|
Rafael Hernandez
|
Cesar Gomez, Rafael Hernandez
|
Quantum deformed magnon kinematics
|
7 pages. Latex. v2: Misprint corrected. Added references to the
previous elliptic uniformization by N. Beisert and the recent one by I.
Kostov, D. Serban and D. Volin
|
JHEP 0703:108,2007
|
10.1088/1126-6708/2007/03/108
| null |
hep-th
| null |
The dispersion relation for planar N=4 supersymmetric Yang-Mills is
identified with the Casimir of a quantum deformed two-dimensional kinematical
symmetry, E_q(1,1). The quantum deformed symmetry algebra is generated by the
momentum, energy and boost, with deformation parameter q=e^{2\pi i/\lambda}.
Representing the boost as the infinitesimal generator for translations on the
rapidity space leads to an elliptic uniformization with crossing
transformations implemented through translations by the elliptic half-periods.
This quantum deformed algebra can be interpreted as the kinematical symmetry of
a discrete integrable model with lattice spacing given by the BMN length
a=2\pi/\sqrt{\lambda}. The interpretation of the boost generator as the corner
transfer matrix is briefly discussed.
|
[
{
"created": "Mon, 22 Jan 2007 16:18:34 GMT",
"version": "v1"
},
{
"created": "Fri, 23 Mar 2007 14:33:45 GMT",
"version": "v2"
}
] |
2010-10-27
|
[
[
"Gomez",
"Cesar",
""
],
[
"Hernandez",
"Rafael",
""
]
] |
The dispersion relation for planar N=4 supersymmetric Yang-Mills is identified with the Casimir of a quantum deformed two-dimensional kinematical symmetry, E_q(1,1). The quantum deformed symmetry algebra is generated by the momentum, energy and boost, with deformation parameter q=e^{2\pi i/\lambda}. Representing the boost as the infinitesimal generator for translations on the rapidity space leads to an elliptic uniformization with crossing transformations implemented through translations by the elliptic half-periods. This quantum deformed algebra can be interpreted as the kinematical symmetry of a discrete integrable model with lattice spacing given by the BMN length a=2\pi/\sqrt{\lambda}. The interpretation of the boost generator as the corner transfer matrix is briefly discussed.
|
1810.09405
|
Runqiu Yang
|
Run-Qiu Yang and Keun-Young Kim
|
Complexity of operators generated by quantum mechanical Hamiltonians
|
A revised version and gives more detailed examples on why
"complexity'' in quantum mechanics and quantum field theory should be
bi-invariant
| null |
10.1007/JHEP03(2019)010
| null |
hep-th quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We propose how to compute the complexity of operators generated by
Hamiltonians in quantum field theory (QFT) and quantum mechanics (QM). The
Hamiltonians in QFT/QM and quantum circuit have a few essential differences,
for which we introduce new principles and methods for complexity. We show that
the complexity geometry corresponding to one-dimensional quadratic Hamiltonians
is equivalent to AdS$_3$ spacetime. Here, the requirement that the complexity
is nonnegative corresponds to the fact that the Hamiltonian is lower bounded
and the speed of a particle is not superluminal. Our proposal proves the
complexity of the operator generated by a free Hamiltonian is zero, as
expected. By studying a non-relativistic particle in compact Riemannian
manifolds we find the complexity is given by the global geometric property of
the space. In particular, we show that in low energy limit the critical
spacetime dimension to ensure the "nonnegative" complexity is the 3+1
dimension.
|
[
{
"created": "Mon, 22 Oct 2018 17:06:07 GMT",
"version": "v1"
},
{
"created": "Mon, 18 Feb 2019 12:26:03 GMT",
"version": "v2"
}
] |
2019-03-27
|
[
[
"Yang",
"Run-Qiu",
""
],
[
"Kim",
"Keun-Young",
""
]
] |
We propose how to compute the complexity of operators generated by Hamiltonians in quantum field theory (QFT) and quantum mechanics (QM). The Hamiltonians in QFT/QM and quantum circuit have a few essential differences, for which we introduce new principles and methods for complexity. We show that the complexity geometry corresponding to one-dimensional quadratic Hamiltonians is equivalent to AdS$_3$ spacetime. Here, the requirement that the complexity is nonnegative corresponds to the fact that the Hamiltonian is lower bounded and the speed of a particle is not superluminal. Our proposal proves the complexity of the operator generated by a free Hamiltonian is zero, as expected. By studying a non-relativistic particle in compact Riemannian manifolds we find the complexity is given by the global geometric property of the space. In particular, we show that in low energy limit the critical spacetime dimension to ensure the "nonnegative" complexity is the 3+1 dimension.
|
0904.3317
|
G\'abor Zsolt T\'oth
|
Gabor Zsolt Toth
|
On some aspects of the definition of scattering states in quantum field
theory
|
20 pages
|
Cent. Eur. J. Phys. 10 (2012) 349-360
|
10.2478/S11534-011-0119-Z
| null |
hep-th hep-ph math-ph math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The problem of extending quantum-mechanical formal scattering theory to a
more general class of models that also includes quantum field theories is
discussed, with the aim of clarifying certain aspects of the definition of
scattering states. As the strong limit is not suitable for the definition of
scattering states in quantum field theory, some other limiting procedure is
needed. Two possibilities are considered, the abelian limit and adiabatic
switching. Formulas for the scattering states based on both methods are
discussed, and it is found that generally there are significant differences
between the two approaches. As an illustration of the application and the
features of these formulas, S-matrix elements and energy corrections in two
quantum field theoretical models are calculated using (generalized)
old-fashioned perturbation theory. The two methods are found to give equivalent
results.
|
[
{
"created": "Tue, 21 Apr 2009 18:55:53 GMT",
"version": "v1"
},
{
"created": "Wed, 23 Dec 2009 18:15:13 GMT",
"version": "v2"
},
{
"created": "Thu, 1 Sep 2011 15:27:54 GMT",
"version": "v3"
},
{
"created": "Tue, 21 Feb 2012 14:23:50 GMT",
"version": "v4"
}
] |
2012-04-17
|
[
[
"Toth",
"Gabor Zsolt",
""
]
] |
The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states based on both methods are discussed, and it is found that generally there are significant differences between the two approaches. As an illustration of the application and the features of these formulas, S-matrix elements and energy corrections in two quantum field theoretical models are calculated using (generalized) old-fashioned perturbation theory. The two methods are found to give equivalent results.
|
hep-th/0101130
|
Jian Dai
|
Jian Dai, Xing-Chang Song (Theory Group, Department of Physics, Peking
University)
|
Noncommutative Geometry of Lattice and Staggered Fermions
|
Latex; 13 pages; no figures. References added. Accepted by Phys.
Lett. B
|
Phys.Lett. B508 (2001) 385-391
|
10.1016/S0370-2693(01)00522-6
| null |
hep-th hep-lat math-ph math.MP
| null |
Differential structure of a d-dimensional lattice, which is essentially a
noncommutative exterior algebra, is defined using reductions in first order and
second order of universal differential calculus in the context of
noncommutative geometry (NCG) developed by Dimakis et al. This differential
structure can be realized adopting a Dirac-Connes operator proposed by us
recently within Connes' NCG. With matrix representations being specified, our
Dirac-Connes operator corresponds to staggered Dirac operator, in the case that
dimension of the lattice equals to 1, 2 and 4.
|
[
{
"created": "Fri, 19 Jan 2001 16:30:42 GMT",
"version": "v1"
},
{
"created": "Wed, 25 Apr 2001 08:44:21 GMT",
"version": "v2"
}
] |
2009-11-07
|
[
[
"Dai",
"Jian",
"",
"Theory Group, Department of Physics, Peking\n University"
],
[
"Song",
"Xing-Chang",
"",
"Theory Group, Department of Physics, Peking\n University"
]
] |
Differential structure of a d-dimensional lattice, which is essentially a noncommutative exterior algebra, is defined using reductions in first order and second order of universal differential calculus in the context of noncommutative geometry (NCG) developed by Dimakis et al. This differential structure can be realized adopting a Dirac-Connes operator proposed by us recently within Connes' NCG. With matrix representations being specified, our Dirac-Connes operator corresponds to staggered Dirac operator, in the case that dimension of the lattice equals to 1, 2 and 4.
|
1901.08922
|
Miguel Tierz
|
David Garc\'ia-Garc\'ia and Miguel Tierz
|
Matrix models for classical groups and Toeplitz$\pm $Hankel minors with
applications to Chern-Simons theory and fermionic models
|
32 pages, v2: Several improvements, including a Conclusions and
Outlook section, added. 36 pages
|
J. Phys. A: Math. Theor. 53 345201 (2020)
|
10.1088/1751-8121/ab9b4d
| null |
hep-th math-ph math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study matrix integration over the classical Lie groups $U(N),Sp(2N),O(2N)$
and $O(2N+1)$, using symmetric function theory and the equivalent formulation
in terms of determinants and minors of Toeplitz$\pm$Hankel matrices. We
establish a number of factorizations and expansions for such integrals, also
with insertions of irreducible characters. As a specific example, we compute
both at finite and large $N$ the partition functions, Wilson loops and Hopf
links of Chern-Simons theory on $S^{3}$ with the aforementioned symmetry
groups. The identities found for the general models translate in this context
to relations between observables of the theory. Finally, we use character
expansions to evaluate averages in random matrix ensembles of Chern-Simons
type, describing the spectra of solvable fermionic models with matrix degrees
of freedom.
|
[
{
"created": "Fri, 25 Jan 2019 15:26:54 GMT",
"version": "v1"
},
{
"created": "Sat, 16 May 2020 03:37:05 GMT",
"version": "v2"
}
] |
2020-10-26
|
[
[
"García-García",
"David",
""
],
[
"Tierz",
"Miguel",
""
]
] |
We study matrix integration over the classical Lie groups $U(N),Sp(2N),O(2N)$ and $O(2N+1)$, using symmetric function theory and the equivalent formulation in terms of determinants and minors of Toeplitz$\pm$Hankel matrices. We establish a number of factorizations and expansions for such integrals, also with insertions of irreducible characters. As a specific example, we compute both at finite and large $N$ the partition functions, Wilson loops and Hopf links of Chern-Simons theory on $S^{3}$ with the aforementioned symmetry groups. The identities found for the general models translate in this context to relations between observables of the theory. Finally, we use character expansions to evaluate averages in random matrix ensembles of Chern-Simons type, describing the spectra of solvable fermionic models with matrix degrees of freedom.
|
1203.6590
|
Carl Bender
|
Carl M. Bender, Daniel W. Hook and S. P. Klevansky
|
Negative-energy PT-symmetric Hamiltonians
|
12 pages, 8 figures
| null |
10.1088/1751-8113/45/44/444003
| null |
hep-th math-ph math.MP quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The non-Hermitian PT-symmetric quantum-mechanical Hamiltonian
$H=p^2+x^2(ix)^\epsilon$ has real, positive, and discrete eigenvalues for all
$\epsilon\geq 0$. These eigenvalues are analytic continuations of the
harmonic-oscillator eigenvalues $E_n=2n+1$ (n=0, 1, 2, 3, ...) at $\epsilon=0$.
However, the harmonic oscillator also has negative eigenvalues $E_n=-2n-1$
(n=0, 1, 2, 3, ...), and one may ask whether it is equally possible to continue
analytically from these eigenvalues. It is shown in this paper that for
appropriate PT-symmetric boundary conditions the Hamiltonian
$H=p^2+x^2(ix)^\epsilon$ also has real and {\it negative} discrete eigenvalues.
The negative eigenvalues fall into classes labeled by the integer N (N=1, 2, 3,
...). For the Nth class of eigenvalues, $\epsilon$ lies in the range
$(4N-6)/3<\epsilon<4N-2$. At the low and high ends of this range, the
eigenvalues are all infinite. At the special intermediate value $\epsilon=2N-2$
the eigenvalues are the negatives of those of the conventional Hermitian
Hamiltonian $H=p^2+x^{2N}$. However, when $\epsilon\neq 2N-2$, there are
infinitely many complex eigenvalues. Thus, while the positive-spectrum sector
of the Hamiltonian $H=p^2+x^2(ix)^\epsilon$ has an unbroken PT symmetry (the
eigenvalues are all real), the negative-spectrum sector of
$H=p^2+x^2(ix)^\epsilon$ has a broken PT symmetry (only some of the eigenvalues
are real).
|
[
{
"created": "Thu, 29 Mar 2012 16:55:09 GMT",
"version": "v1"
}
] |
2014-08-28
|
[
[
"Bender",
"Carl M.",
""
],
[
"Hook",
"Daniel W.",
""
],
[
"Klevansky",
"S. P.",
""
]
] |
The non-Hermitian PT-symmetric quantum-mechanical Hamiltonian $H=p^2+x^2(ix)^\epsilon$ has real, positive, and discrete eigenvalues for all $\epsilon\geq 0$. These eigenvalues are analytic continuations of the harmonic-oscillator eigenvalues $E_n=2n+1$ (n=0, 1, 2, 3, ...) at $\epsilon=0$. However, the harmonic oscillator also has negative eigenvalues $E_n=-2n-1$ (n=0, 1, 2, 3, ...), and one may ask whether it is equally possible to continue analytically from these eigenvalues. It is shown in this paper that for appropriate PT-symmetric boundary conditions the Hamiltonian $H=p^2+x^2(ix)^\epsilon$ also has real and {\it negative} discrete eigenvalues. The negative eigenvalues fall into classes labeled by the integer N (N=1, 2, 3, ...). For the Nth class of eigenvalues, $\epsilon$ lies in the range $(4N-6)/3<\epsilon<4N-2$. At the low and high ends of this range, the eigenvalues are all infinite. At the special intermediate value $\epsilon=2N-2$ the eigenvalues are the negatives of those of the conventional Hermitian Hamiltonian $H=p^2+x^{2N}$. However, when $\epsilon\neq 2N-2$, there are infinitely many complex eigenvalues. Thus, while the positive-spectrum sector of the Hamiltonian $H=p^2+x^2(ix)^\epsilon$ has an unbroken PT symmetry (the eigenvalues are all real), the negative-spectrum sector of $H=p^2+x^2(ix)^\epsilon$ has a broken PT symmetry (only some of the eigenvalues are real).
|
hep-th/9408092
|
Mike Freeman
|
Michael Freeman
|
Conserved charges and soliton solutions in affine Toda theory
|
18 pages, plain tex, minor changes, references added
|
Nucl.Phys. B433 (1995) 657-670
|
10.1016/0550-3213(94)00519-K
|
KCL-TH-94-8
|
hep-th
| null |
We study the conserved charges of affine Toda field theories by making use of
the conformally invariant extension of these theories. We compute the values of
all charges for the single soliton solutions, and show that these are related
to eigenvectors of the Cartan matrix of the finite-dimensional Lie algebra
underlying the theory.
|
[
{
"created": "Tue, 16 Aug 1994 15:35:44 GMT",
"version": "v1"
},
{
"created": "Mon, 7 Nov 1994 15:01:10 GMT",
"version": "v2"
}
] |
2009-10-28
|
[
[
"Freeman",
"Michael",
""
]
] |
We study the conserved charges of affine Toda field theories by making use of the conformally invariant extension of these theories. We compute the values of all charges for the single soliton solutions, and show that these are related to eigenvectors of the Cartan matrix of the finite-dimensional Lie algebra underlying the theory.
|
hep-th/9111063
|
T. R. Govindarajan
|
R. K. Kaul and T. R. Govindarajan
|
Three Dimensional Chern-Simons Theory as a Theory of Knots and Links
|
45 pages (without figures)
|
Nucl.Phys. B380 (1992) 293-336
|
10.1016/0550-3213(92)90524-F
| null |
hep-th math.QA
| null |
Three dimensional SU(2) Chern-Simons theory has been studied as a topological
field theory to provide a field theoretic description of knots and links in
three dimensions. A systematic method has been developed to obtain the
link-invariants within this field theoretic framework. The monodromy properties
of the correlators of the associated Wess-Zumino SU(2)$_k$ conformal field
theory on a two-dimensional sphere prove to be useful tools. The method is
simple enough to yield a whole variety of new knot invariants of which the
Jones polynomials are the simplest example.
|
[
{
"created": "Thu, 28 Nov 1991 13:41:35 GMT",
"version": "v1"
}
] |
2009-10-22
|
[
[
"Kaul",
"R. K.",
""
],
[
"Govindarajan",
"T. R.",
""
]
] |
Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants within this field theoretic framework. The monodromy properties of the correlators of the associated Wess-Zumino SU(2)$_k$ conformal field theory on a two-dimensional sphere prove to be useful tools. The method is simple enough to yield a whole variety of new knot invariants of which the Jones polynomials are the simplest example.
|
hep-th/9801129
|
Michael Bordag
|
M Bordag and J Lindig
|
Radiative Correction to the Casimir Force on a Sphere
|
26 pages, 2 figures, subm. to Phys. Rev
|
Phys.Rev.D58:045003,1998
|
10.1103/PhysRevD.58.045003
| null |
hep-th
| null |
The first radiative correction to the Casimir energy of a perfectly
conducting spherical shell is calculated. The calculation is performed in the
framework of covariant perturbation theory with the boundary conditions
implemented as constraints. The formalism is briefly reviewed and its use is
explained by deriving the known results for two parallel planes.
The ultraviolet divergencies are shown to have the same structure as those
for a massive field in zeroth order of $\alpha$. In the zeta-functional
regularization employed by us no divergencies appear.
If the radius of the sphere is large compared to the Compton wavelength of
the electron the radiative correction is of order $\alpha/(R^2m_e)$ and
contains a logarithmic dependence on $m_eR$. It has the opposite sign but the
same order of magnitude as in the case of two parallel planes.
|
[
{
"created": "Mon, 19 Jan 1998 15:30:37 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Bordag",
"M",
""
],
[
"Lindig",
"J",
""
]
] |
The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is calculated. The calculation is performed in the framework of covariant perturbation theory with the boundary conditions implemented as constraints. The formalism is briefly reviewed and its use is explained by deriving the known results for two parallel planes. The ultraviolet divergencies are shown to have the same structure as those for a massive field in zeroth order of $\alpha$. In the zeta-functional regularization employed by us no divergencies appear. If the radius of the sphere is large compared to the Compton wavelength of the electron the radiative correction is of order $\alpha/(R^2m_e)$ and contains a logarithmic dependence on $m_eR$. It has the opposite sign but the same order of magnitude as in the case of two parallel planes.
|
0708.3045
|
Heinz Rothe J
|
Heinz J. Rothe, Klaus D. Rothe
|
From the BRST invariant Hamiltonian to the Field-Antifield Formalism
|
14 pages
|
Annals Phys.323:1384-1396,2008
|
10.1016/j.aop.2007.08.006
|
HD-THEP-07-13
|
hep-th
| null |
We study the relation between the lagrangian field-antifield formalism and
the BRST invariant phase space formulation of gauge theories. Starting from the
Batalin-Fradkin-Vilkovisky unitarized action, we demonstrate in a deductive way
the equivalence of the phase space, and the lagrangian field-antifield
partition functions for the case of irreducible first rank theories.
|
[
{
"created": "Wed, 22 Aug 2007 16:20:10 GMT",
"version": "v1"
}
] |
2009-11-18
|
[
[
"Rothe",
"Heinz J.",
""
],
[
"Rothe",
"Klaus D.",
""
]
] |
We study the relation between the lagrangian field-antifield formalism and the BRST invariant phase space formulation of gauge theories. Starting from the Batalin-Fradkin-Vilkovisky unitarized action, we demonstrate in a deductive way the equivalence of the phase space, and the lagrangian field-antifield partition functions for the case of irreducible first rank theories.
|
2211.05804
|
Lara Anderson
|
Lara B. Anderson, Callum R. Brodie, James Gray
|
Branes and Bundles through Conifold Transitions and Dualities in
Heterotic String Theory
|
49 pages, 6 figures
| null | null | null |
hep-th
|
http://creativecommons.org/licenses/by/4.0/
|
Geometric transitions between Calabi-Yau manifolds have proven to be a
powerful tool in exploring the intricate and interconnected vacuum structure of
string compactifications. However, their role in N=1, 4-dimensional string
compactifications remains relatively unexplored. In this work we present a
novel proposal for transitioning the background geometry (including NS5-branes
and holomorphic, slope-stable vector bundles) of 4-dimensional, N=1 heterotic
string compactifications through a conifold transition connecting Calabi-Yau
threefolds. Our proposal is geometric in nature but informed by the heterotic
effective theory. Central to this study is a description of how the cotangent
bundles of the deformation and resolution manifolds in the conifold can be
connected by an apparent small instanton transition with a 5-brane wrapping the
small resolution curves. We show that by a "pair creation" process 5-branes can
be generated simultaneously in the gauge and gravitational sectors and used to
describe a coupled minimal change in the manifold and gauge sector. This
observation leads us to propose dualities for 5-branes and gauge bundles in
heterotic conifolds which we then confirm at the level of spectrum in large
classes of examples. While the 5-brane duality is novel, we observe that the
bundle correspondence has appeared before in the Target Space Duality exhibited
by (0,2) GLSMs. Thus our work provides a geometric explanation of (0,2) Target
Space Duality.
|
[
{
"created": "Thu, 10 Nov 2022 19:00:28 GMT",
"version": "v1"
}
] |
2022-11-14
|
[
[
"Anderson",
"Lara B.",
""
],
[
"Brodie",
"Callum R.",
""
],
[
"Gray",
"James",
""
]
] |
Geometric transitions between Calabi-Yau manifolds have proven to be a powerful tool in exploring the intricate and interconnected vacuum structure of string compactifications. However, their role in N=1, 4-dimensional string compactifications remains relatively unexplored. In this work we present a novel proposal for transitioning the background geometry (including NS5-branes and holomorphic, slope-stable vector bundles) of 4-dimensional, N=1 heterotic string compactifications through a conifold transition connecting Calabi-Yau threefolds. Our proposal is geometric in nature but informed by the heterotic effective theory. Central to this study is a description of how the cotangent bundles of the deformation and resolution manifolds in the conifold can be connected by an apparent small instanton transition with a 5-brane wrapping the small resolution curves. We show that by a "pair creation" process 5-branes can be generated simultaneously in the gauge and gravitational sectors and used to describe a coupled minimal change in the manifold and gauge sector. This observation leads us to propose dualities for 5-branes and gauge bundles in heterotic conifolds which we then confirm at the level of spectrum in large classes of examples. While the 5-brane duality is novel, we observe that the bundle correspondence has appeared before in the Target Space Duality exhibited by (0,2) GLSMs. Thus our work provides a geometric explanation of (0,2) Target Space Duality.
|
hep-th/9605128
|
Thomas Thiemann
|
Abhay Ashtekar, Jurek Lewandowski, Donald Marolf, Jos\'e Mour\~ao,
Thomas Thiemann
|
Closed formula for Wilson loops for $SU(N)$ Quantum Yang-Mills Theory in
two dimensions
|
31 pages, Latex, no figures
|
J.Math.Phys. 38 (1997) 5453-5482
|
10.1063/1.532146
|
HUTMP-96/B-351, CGPG-94/4-2
|
hep-th
| null |
A closed expression of the Euclidean Wilson-loop functionals is derived for
pure Yang-Mills continuum theories with gauge groups $SU(N)$ and $U(1)$ and
space-time topologies $\Rl^1\times\Rl^1$ and $\Rl^1\times S^1$. (For the $U(1)$
theory, we also consider the $S^1\times S^1$ topology.) The treatment is
rigorous, manifestly gauge invariant, manifestly invariant under area
preserving diffeomorphisms and handles all (piecewise analytic) loops in one
stroke. Equivalence between the resulting Euclidean theory and and the
Hamiltonian framework is then established. Finally, an extension of the
Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are
satisfied for the present model.
|
[
{
"created": "Sat, 18 May 1996 00:18:03 GMT",
"version": "v1"
}
] |
2009-10-30
|
[
[
"Ashtekar",
"Abhay",
""
],
[
"Lewandowski",
"Jurek",
""
],
[
"Marolf",
"Donald",
""
],
[
"Mourão",
"José",
""
],
[
"Thiemann",
"Thomas",
""
]
] |
A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang-Mills continuum theories with gauge groups $SU(N)$ and $U(1)$ and space-time topologies $\Rl^1\times\Rl^1$ and $\Rl^1\times S^1$. (For the $U(1)$ theory, we also consider the $S^1\times S^1$ topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied for the present model.
|
hep-th/0312135
|
Annamaria Sinkovics
|
Jan de Boer, Annamaria Sinkovics, Erik Verlinde and Jung-Tay Yee
|
String Interactions in c=1 Matrix Model
|
27 pages, 1 figure
|
JHEP 0403 (2004) 023
|
10.1088/1126-6708/2004/03/023
|
ITFA-2003-56, KIAS-P03089
|
hep-th
| null |
We study string interactions in the fermionic formulation of the c=1 matrix
model. We give a precise nonperturbative description of the rolling tachyon
state in the matrix model, and discuss S-matrix elements of the c=1 string. As
a first step to study string interactions, we compute the interaction of two
decaying D0-branes in terms of free fermions. This computation is compared with
the string theory cylinder diagram using the rolling tachyon ZZ boundary
states.
|
[
{
"created": "Fri, 12 Dec 2003 13:55:25 GMT",
"version": "v1"
}
] |
2009-11-10
|
[
[
"de Boer",
"Jan",
""
],
[
"Sinkovics",
"Annamaria",
""
],
[
"Verlinde",
"Erik",
""
],
[
"Yee",
"Jung-Tay",
""
]
] |
We study string interactions in the fermionic formulation of the c=1 matrix model. We give a precise nonperturbative description of the rolling tachyon state in the matrix model, and discuss S-matrix elements of the c=1 string. As a first step to study string interactions, we compute the interaction of two decaying D0-branes in terms of free fermions. This computation is compared with the string theory cylinder diagram using the rolling tachyon ZZ boundary states.
|
hep-th/0509028
|
Jixiang Fu
|
Ji-Xiang Fu and Shing-Tung Yau
|
Existence of Supersymmetric Hermitian Metrics with Torsion on
Non-Kaehler Manifolds
|
48 pages
| null | null | null |
hep-th
| null |
We proved the existence of supersymmetric Hermitian metrics with torsion on a
class of non-Kaehler manifolds.
|
[
{
"created": "Fri, 2 Sep 2005 21:57:13 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Fu",
"Ji-Xiang",
""
],
[
"Yau",
"Shing-Tung",
""
]
] |
We proved the existence of supersymmetric Hermitian metrics with torsion on a class of non-Kaehler manifolds.
|
2012.10454
|
Miguel F. Paulos
|
Miguel F. Paulos
|
Dispersion relations and exact bounds on CFT correlators
|
46 pages + appendices
| null |
10.1007/JHEP08(2021)166
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We derive new crossing-symmetric dispersion formulae for CFT correlators
restricted to the line. The formulae are equivalent to the sum rules implied by
what we call master functionals, which are analytic extremal functionals which
act on the crossing equation. The dispersion relations provide an equivalent
formulation of the constraints of the Polyakov bootstrap and hence of crossing
symmetry on the line. The built in positivity properties imply simple and exact
lower and upper bounds on the values of general CFT correlators on the
Euclidean section, which are saturated by generalized free fields. Besides
bounds on correlators, we apply this technology to determine new universal
constraints on the Regge limit of arbitrary CFTs and obtain very simple and
accurate representations of the 3d Ising spin correlator.
|
[
{
"created": "Fri, 18 Dec 2020 19:00:01 GMT",
"version": "v1"
}
] |
2021-09-15
|
[
[
"Paulos",
"Miguel F.",
""
]
] |
We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on the crossing equation. The dispersion relations provide an equivalent formulation of the constraints of the Polyakov bootstrap and hence of crossing symmetry on the line. The built in positivity properties imply simple and exact lower and upper bounds on the values of general CFT correlators on the Euclidean section, which are saturated by generalized free fields. Besides bounds on correlators, we apply this technology to determine new universal constraints on the Regge limit of arbitrary CFTs and obtain very simple and accurate representations of the 3d Ising spin correlator.
|
1607.02083
|
Dmitriy Pak
|
Youngman Kim, Bum-Hoon Lee, D.G. Pak, Chanyong Park, Takuya Tsukioka
|
Quantum stability of non-linear wave type solutions with intrinsic mass
parameter in QCD
|
13 pages, 7 figures, final version accepted for publication in Phys.
Rev. D, minor corrections
|
Phys. Rev. D 96, 054025 (2017)
|
10.1103/PhysRevD.96.054025
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The problem of existence of a stable vacuum field in a pure quantum
chromodynamics (QCD) is revised. Our approach is based on using classical
stationary non-linear wave type solutions with intrinsic mass scale parameter.
Such solutions can be treated as quantum mechanical wave functions describing
massive spinless states in quantum theory. We verify whether non-linear wave
type solutions can form a stable vacuum field background within the framework
of effective action formalism. We demonstrate that there is a special class of
stationary generalized Wu-Yang monopole solutions which are stable against
quantum gluon fluctuations.
|
[
{
"created": "Thu, 7 Jul 2016 17:00:04 GMT",
"version": "v1"
},
{
"created": "Sat, 30 Jul 2016 04:36:23 GMT",
"version": "v2"
},
{
"created": "Fri, 3 Mar 2017 11:12:32 GMT",
"version": "v3"
},
{
"created": "Tue, 25 Jul 2017 03:16:49 GMT",
"version": "v4"
},
{
"created": "Tue, 5 Sep 2017 06:38:39 GMT",
"version": "v5"
},
{
"created": "Fri, 15 Sep 2017 00:40:13 GMT",
"version": "v6"
}
] |
2017-10-02
|
[
[
"Kim",
"Youngman",
""
],
[
"Lee",
"Bum-Hoon",
""
],
[
"Pak",
"D. G.",
""
],
[
"Park",
"Chanyong",
""
],
[
"Tsukioka",
"Takuya",
""
]
] |
The problem of existence of a stable vacuum field in a pure quantum chromodynamics (QCD) is revised. Our approach is based on using classical stationary non-linear wave type solutions with intrinsic mass scale parameter. Such solutions can be treated as quantum mechanical wave functions describing massive spinless states in quantum theory. We verify whether non-linear wave type solutions can form a stable vacuum field background within the framework of effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions which are stable against quantum gluon fluctuations.
|
1111.6507
|
Carlos Scarinci
|
Carlos Scarinci and Kirill Krasnov
|
The Universal Phase Space of AdS3 Gravity
|
41 pages, 2 figures, revised version accepted for publication in
Commun.Math.Phys
|
Commun.Math.Phys.322:167-205,2013
|
10.1007/s00220-012-1655-0
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We describe what can be called the "universal" phase space of AdS3 gravity,
in which the moduli spaces of globally hyperbolic AdS spacetimes with compact
spatial sections, as well as the moduli spaces of multi-black-hole spacetimes
are realized as submanifolds. The universal phase space is parametrized by two
copies of the Universal Teichm\"uller space T(1) and is obtained from the
correspondence between maximal surfaces in AdS3 and quasisymmetric
homeomorphisms of the unit circle. We also relate our parametrization to the
Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the
holographic (Fefferman-Graham) description. In particular, we obtain a relation
between the generators of quasiconformal deformations in each T(1) sector and
the chiral Brown-Henneaux vector fields. We also relate the charges arising in
the holographic description (such as the mass and angular momentum of an AdS3
spacetime) to the periods of the quadratic differentials arising via the Bers
embedding of T(1)xT(1). Our construction also yields a symplectic map from
T*T(1) to T(1)xT(1) generalizing the well-known Mess map in the compact spatial
surface setting.
|
[
{
"created": "Mon, 28 Nov 2011 16:31:45 GMT",
"version": "v1"
},
{
"created": "Mon, 4 Feb 2013 01:13:43 GMT",
"version": "v2"
}
] |
2013-07-09
|
[
[
"Scarinci",
"Carlos",
""
],
[
"Krasnov",
"Kirill",
""
]
] |
We describe what can be called the "universal" phase space of AdS3 gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact spatial sections, as well as the moduli spaces of multi-black-hole spacetimes are realized as submanifolds. The universal phase space is parametrized by two copies of the Universal Teichm\"uller space T(1) and is obtained from the correspondence between maximal surfaces in AdS3 and quasisymmetric homeomorphisms of the unit circle. We also relate our parametrization to the Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the holographic (Fefferman-Graham) description. In particular, we obtain a relation between the generators of quasiconformal deformations in each T(1) sector and the chiral Brown-Henneaux vector fields. We also relate the charges arising in the holographic description (such as the mass and angular momentum of an AdS3 spacetime) to the periods of the quadratic differentials arising via the Bers embedding of T(1)xT(1). Our construction also yields a symplectic map from T*T(1) to T(1)xT(1) generalizing the well-known Mess map in the compact spatial surface setting.
|
hep-th/9612131
|
Yaron Oz
|
Jan de Boer, Kentaro Hori, Hirosi Ooguri, Yaron Oz and Zheng Yin
|
Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane
Moduli Spaces
|
36 pages, 16 figures, LaTex 2
|
Nucl.Phys.B493:148-176,1997
|
10.1016/S0550-3213(97)00115-6
|
LBNL-039707, UCB-PTH-96/58
|
hep-th
| null |
We construct intersecting D-brane configurations that encode the gauge groups
and field content of dual N=4 supersymmetric gauge theories in three
dimensions. The duality which exchanges the Coulomb and Higgs branches and the
Fayet-Iliopoulos and mass parameters is derived from the SL(2,Z) symmetry of
the type IIB string. Using the D-brane configurations we construct explicitly
this mirror map between the dual theories and study the instanton corrections
in the D-brane worldvolume theory via open string instantons. A general
procedure to obtain mirror pairs is presented and illustrated. We encounter
transitions among different field theories that correspond to smooth movements
in the D-brane moduli space. We discuss the relation between the duality of the
gauge theories and the level-rank duality of affine Lie algebras. Examples of
other dual theories are presented and explained via T-duality and extremal
transitions in type II string compactifications. Finally we discuss a second
way to study instanton corrections in the gauge theory, by wrapping five-branes
around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.
|
[
{
"created": "Thu, 12 Dec 1996 23:10:50 GMT",
"version": "v1"
}
] |
2009-09-17
|
[
[
"de Boer",
"Jan",
""
],
[
"Hori",
"Kentaro",
""
],
[
"Ooguri",
"Hirosi",
""
],
[
"Oz",
"Yaron",
""
],
[
"Yin",
"Zheng",
""
]
] |
We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N=4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL(2,Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane worldvolume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping five-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.
|
2207.13207
|
Hanif Golchin
|
Hanif Golchin
|
Regular Black Holes: Entropy Products and Central Charges
|
minor corrections
| null |
10.1103/PhysRevD.106.066007
| null |
hep-th gr-qc
|
http://creativecommons.org/licenses/by/4.0/
|
In this paper for variety types of regular black hole solutions, we
investigate the entropy product of inner and outer horizons. Similar to
singular black holes, for the regular ones we find that universality (mass
independence) of the entropy product is true for some solutions and it fails
for some others. In the case of regular black holes that respect the
universality, we read central charges of the dual CFTs from the entropy
product, according to the Thermodynamics method introduced in
\cite{Chen:2013rb}. For these solutions we also calculate central charges,
using the asymptotic symmetry group formalism. The results of these two
approaches are the same, which means that universality of the entropy product
provides a simple method to find central charges of the dual CFTs.
|
[
{
"created": "Tue, 26 Jul 2022 22:54:03 GMT",
"version": "v1"
},
{
"created": "Wed, 3 Aug 2022 11:40:13 GMT",
"version": "v2"
}
] |
2022-10-05
|
[
[
"Golchin",
"Hanif",
""
]
] |
In this paper for variety types of regular black hole solutions, we investigate the entropy product of inner and outer horizons. Similar to singular black holes, for the regular ones we find that universality (mass independence) of the entropy product is true for some solutions and it fails for some others. In the case of regular black holes that respect the universality, we read central charges of the dual CFTs from the entropy product, according to the Thermodynamics method introduced in \cite{Chen:2013rb}. For these solutions we also calculate central charges, using the asymptotic symmetry group formalism. The results of these two approaches are the same, which means that universality of the entropy product provides a simple method to find central charges of the dual CFTs.
|
hep-th/9812150
|
Jacques Bros
|
J. Bros, G.A. Viano
|
Complex Angular Momentum in General Quantum Field Theory
|
86 pages, 9 figures, tcilatex
|
Annales Henri Poincare 1 (2006) 101-172
| null |
SPTh t98/142
|
hep-th
| null |
It is proven that for each given two-field channel - called the
``t-channel''- with (off-shell) ``scattering angle'' $\Theta_t$, the four-point
Green's function of any scalar Quantum Fields satisfying the basic principles
of locality, spectral condition together with temperateness admits a
Laplace-type transform in the corresponding complex angular momentum variable
$\lambda_t$, dual to $\Theta_t$. This transform enjoys the following
properties: a) it is holomorphic in a half-plane of the form $Re \lambda_t >
m$, where m is a certain ``degree of temperateness'' of the fields considered,
b) it is in one-to-one (invertible) correspondence with the (off-shell)
``absorptive parts'' in the crossed two-field channels, c) it extrapolates in a
canonical way to complex values of the angular momentum the coefficients of the
(off-shell) t-channel partial-wave expansion of the Euclidean four-point
function of the fields. These properties are established for all space-time
dimensions d+1 with $d \ge 2$.
|
[
{
"created": "Thu, 17 Dec 1998 16:54:54 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Bros",
"J.",
""
],
[
"Viano",
"G. A.",
""
]
] |
It is proven that for each given two-field channel - called the ``t-channel''- with (off-shell) ``scattering angle'' $\Theta_t$, the four-point Green's function of any scalar Quantum Fields satisfying the basic principles of locality, spectral condition together with temperateness admits a Laplace-type transform in the corresponding complex angular momentum variable $\lambda_t$, dual to $\Theta_t$. This transform enjoys the following properties: a) it is holomorphic in a half-plane of the form $Re \lambda_t > m$, where m is a certain ``degree of temperateness'' of the fields considered, b) it is in one-to-one (invertible) correspondence with the (off-shell) ``absorptive parts'' in the crossed two-field channels, c) it extrapolates in a canonical way to complex values of the angular momentum the coefficients of the (off-shell) t-channel partial-wave expansion of the Euclidean four-point function of the fields. These properties are established for all space-time dimensions d+1 with $d \ge 2$.
|
hep-th/9803249
|
Michael Bershadsky
|
Michael Bershadsky and Andrei Johansen
|
Large N limit of orbifold field theories
|
12 pages, 3 figures, harvmac. Minor changes
|
Nucl.Phys.B536:141-148,1998
|
10.1016/S0550-3213(98)00526-4
|
HUTP-98/A038
|
hep-th
| null |
We consider certain orbifoldization of the ${\cal N}=4$ field theories that
leads to ${\cal N}=2,1,0$ field theories in 4 dimensions. These theories were
recently analyzed using the string theory perturbation technique. It was found
that in the large $N$ limit all correlation functions of the orbifold theories
coincide with those of ${\cal N}=4$, modulo the rescaling of the gauge coupling
constant. In this paper we repeat the same analysis using the field theoretical
language.
|
[
{
"created": "Mon, 30 Mar 1998 18:31:16 GMT",
"version": "v1"
},
{
"created": "Thu, 28 May 1998 17:08:07 GMT",
"version": "v2"
}
] |
2008-11-26
|
[
[
"Bershadsky",
"Michael",
""
],
[
"Johansen",
"Andrei",
""
]
] |
We consider certain orbifoldization of the ${\cal N}=4$ field theories that leads to ${\cal N}=2,1,0$ field theories in 4 dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in the large $N$ limit all correlation functions of the orbifold theories coincide with those of ${\cal N}=4$, modulo the rescaling of the gauge coupling constant. In this paper we repeat the same analysis using the field theoretical language.
|
hep-th/9608103
|
Azakov Siyavush
|
Azakov S.I
|
The Schwinger model on the Torus
|
Latex file: 40 pages
|
Fortsch.Phys. 45 (1997) 589-626
| null |
IC/96/138
|
hep-th
| null |
The classical and quantum aspects of the Schwinger model on the torus are
considered. First we find explicitly all zero modes of the Dirac operator in
the topological sectors with nontrivial Chern index and is spectrum. In the
second part we determine the regularized effective action and discuss the
propagators related to it.
Finally we calculate the gauge invariant averages of the fermion bilinears
and correlation functions of currents and densities. We show that in the
infinite volume limit the well-known result for the chiral condensate can be
obtained and the clustering property can be established.
|
[
{
"created": "Thu, 15 Aug 1996 18:29:11 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"S.",
"Azakov",
"I"
]
] |
The classical and quantum aspects of the Schwinger model on the torus are considered. First we find explicitly all zero modes of the Dirac operator in the topological sectors with nontrivial Chern index and is spectrum. In the second part we determine the regularized effective action and discuss the propagators related to it. Finally we calculate the gauge invariant averages of the fermion bilinears and correlation functions of currents and densities. We show that in the infinite volume limit the well-known result for the chiral condensate can be obtained and the clustering property can be established.
|
1401.3996
|
Victor Afonso
|
Victor I. Afonso and Diego J. Cirilo-Lombardo
|
Geometric Aspects of the `Deformation Method'
|
9 pages, 9 figures
| null | null | null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
At the classical level, redefinitions of the field content of a Lagrangian
allow to rewrite an interacting model on a flat target space, in the form of a
free field model (no potential term) on a curved target space. In the present
work we extend the idea of the `deformation method' introduced in
\cite{defmet}, to show that it is possible to write an explicit correspondence
between the metrics of the curved target spaces that arise in the free versions
of distinct scalar field models. This is accomplished by obtaining an explicit
relation between the map function linking the fields and the free models'
metrics. By considering complex and even quaternionic field models, we extend
the procedure --initially proposed for models of a single scalar field-- to
systems with a content of two and four (despite constrained) real fields,
respectively, widening the range of applicability. We also analyze
supersymmetric models to illustrate more possibilities. In particular, we show
how to relate a flat Minkowskian metric to a Fubini-Study space.
|
[
{
"created": "Thu, 16 Jan 2014 11:45:32 GMT",
"version": "v1"
},
{
"created": "Wed, 2 Sep 2015 15:56:23 GMT",
"version": "v2"
}
] |
2015-09-03
|
[
[
"Afonso",
"Victor I.",
""
],
[
"Cirilo-Lombardo",
"Diego J.",
""
]
] |
At the classical level, redefinitions of the field content of a Lagrangian allow to rewrite an interacting model on a flat target space, in the form of a free field model (no potential term) on a curved target space. In the present work we extend the idea of the `deformation method' introduced in \cite{defmet}, to show that it is possible to write an explicit correspondence between the metrics of the curved target spaces that arise in the free versions of distinct scalar field models. This is accomplished by obtaining an explicit relation between the map function linking the fields and the free models' metrics. By considering complex and even quaternionic field models, we extend the procedure --initially proposed for models of a single scalar field-- to systems with a content of two and four (despite constrained) real fields, respectively, widening the range of applicability. We also analyze supersymmetric models to illustrate more possibilities. In particular, we show how to relate a flat Minkowskian metric to a Fubini-Study space.
|
2008.11307
|
Alexis Roa Aguirre
|
A. R. Aguirre, E. S. Souza
|
Extended multi-scalar field theories in (1+1) dimensions
|
49 pages, 14 figures
|
Eur. Phys. J. C (2020) 80:1143
|
10.1140/epjc/s10052-020-08724-y
| null |
hep-th math-ph math.MP nlin.SI
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We present the explicit construction of some multi-scalar field theories in
(1+1) dimensions supporting BPS (Bogomol'nyi--Prasad--Sommerfield) kink
solutions. The construction is based on the ideas of the so-called extension
method. In particular, several new interesting two-scalar and three-scalar
field theories are explicitly constructed from non-trivial couplings between
well-known one-scalar field theories. The BPS solutions of the original
one-field systems will be also BPS solutions of the multi-scalar system by
construction, and therefore we will analyse their linear stability properties
for the constructed models.
|
[
{
"created": "Tue, 25 Aug 2020 23:30:18 GMT",
"version": "v1"
}
] |
2020-12-16
|
[
[
"Aguirre",
"A. R.",
""
],
[
"Souza",
"E. S.",
""
]
] |
We present the explicit construction of some multi-scalar field theories in (1+1) dimensions supporting BPS (Bogomol'nyi--Prasad--Sommerfield) kink solutions. The construction is based on the ideas of the so-called extension method. In particular, several new interesting two-scalar and three-scalar field theories are explicitly constructed from non-trivial couplings between well-known one-scalar field theories. The BPS solutions of the original one-field systems will be also BPS solutions of the multi-scalar system by construction, and therefore we will analyse their linear stability properties for the constructed models.
|
1306.1546
|
Benjamin Koch
|
Benjamin Koch and Frank Saueressig
|
Structural aspects of asymptotically safe black holes
|
28 pages 13 figures
| null |
10.1088/0264-9381/31/1/015006
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study the quantum modifications of classical, spherically symmetric
Schwarzschild (Anti-) de Sitter black holes within Quantum Einstein Gravity.
The quantum effects are incorporated through the running coupling constants
$G_k$ and $\Lambda_k$, computed within the exact renormalization group
approach, and a common scale-setting procedure. We find that, in contrast to
common intuition, it is actually the cosmological constant that determines the
short-distance structure of the RG-improved black hole: in the asymptotic UV
the structure of the quantum solutions is universal and given by the classical
Schwarzschild-de Sitter solution, entailing a self-similarity between the
classical and quantum regime. As a consequence asymptotically safe black holes
evaporate completely and no Planck-size remnants are formed. Moreover, the
thermodynamic entropy of the critical Nariai-black hole is shown to agree with
the microstate count based on the effective average action, suggesting that the
entropy originates from quantum fluctuations around the mean-field geometry.
|
[
{
"created": "Thu, 6 Jun 2013 20:31:20 GMT",
"version": "v1"
},
{
"created": "Thu, 10 Oct 2013 15:29:58 GMT",
"version": "v2"
}
] |
2015-06-16
|
[
[
"Koch",
"Benjamin",
""
],
[
"Saueressig",
"Frank",
""
]
] |
We study the quantum modifications of classical, spherically symmetric Schwarzschild (Anti-) de Sitter black holes within Quantum Einstein Gravity. The quantum effects are incorporated through the running coupling constants $G_k$ and $\Lambda_k$, computed within the exact renormalization group approach, and a common scale-setting procedure. We find that, in contrast to common intuition, it is actually the cosmological constant that determines the short-distance structure of the RG-improved black hole: in the asymptotic UV the structure of the quantum solutions is universal and given by the classical Schwarzschild-de Sitter solution, entailing a self-similarity between the classical and quantum regime. As a consequence asymptotically safe black holes evaporate completely and no Planck-size remnants are formed. Moreover, the thermodynamic entropy of the critical Nariai-black hole is shown to agree with the microstate count based on the effective average action, suggesting that the entropy originates from quantum fluctuations around the mean-field geometry.
|
0803.1565
|
Samuel Monnier
|
Samuel Monnier
|
Kondo flow invariants, twisted K-theory and Ramond-Ramond charges
|
58 pages. V4 : Problem with the bibliography corrected
|
JHEP0806:022,2008
|
10.1088/1126-6708/2008/06/022
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We take a worldsheet point of view on the relation between Ramond-Ramond
charges, invariants of boundary renormalization group flows and K-theory. In
compact super Wess-Zumino-Witten models, we show how to associate invariants of
the generalized Kondo renormalization group flows to a given supersymmetric
boundary state. The procedure involved is reminiscent of the way one can probe
the Ramond-Ramond charge carried by a D-brane in conformal field theory, and
the set of these invariants is isomorphic to the twisted K-theory of the Lie
group. We construct various supersymmetric boundary states, and we compute the
charges of the corresponding D-branes, disproving two conjectures on this
subject. We find a complete agreement between our algebraic charges and the
geometry of the D-branes.
|
[
{
"created": "Tue, 11 Mar 2008 19:35:50 GMT",
"version": "v1"
},
{
"created": "Fri, 14 Mar 2008 09:59:45 GMT",
"version": "v2"
},
{
"created": "Sun, 25 May 2008 16:18:50 GMT",
"version": "v3"
},
{
"created": "Sun, 6 Jul 2008 14:16:43 GMT",
"version": "v4"
}
] |
2008-11-26
|
[
[
"Monnier",
"Samuel",
""
]
] |
We take a worldsheet point of view on the relation between Ramond-Ramond charges, invariants of boundary renormalization group flows and K-theory. In compact super Wess-Zumino-Witten models, we show how to associate invariants of the generalized Kondo renormalization group flows to a given supersymmetric boundary state. The procedure involved is reminiscent of the way one can probe the Ramond-Ramond charge carried by a D-brane in conformal field theory, and the set of these invariants is isomorphic to the twisted K-theory of the Lie group. We construct various supersymmetric boundary states, and we compute the charges of the corresponding D-branes, disproving two conjectures on this subject. We find a complete agreement between our algebraic charges and the geometry of the D-branes.
|
hep-th/9303163
|
Judy Mack
|
C.R. Hagen and E.C.G. Sudarshan
|
Comment on Operator Algebra in Chern-Simons Theory on a Torus
|
4 pages
|
Phys.Rev.Lett. 74 (1995) 1032
|
10.1103/PhysRevLett.74.1032
|
UR1308, ER-40685-757
|
hep-th
| null |
It is shown that "nonintegrable phases of Wilson line integrals" are not true
dynamical variables in Chern-Simons field theory.
|
[
{
"created": "Mon, 29 Mar 1993 19:43:00 GMT",
"version": "v1"
},
{
"created": "Tue, 30 Mar 1993 13:26:00 GMT",
"version": "v2"
}
] |
2009-10-22
|
[
[
"Hagen",
"C. R.",
""
],
[
"Sudarshan",
"E. C. G.",
""
]
] |
It is shown that "nonintegrable phases of Wilson line integrals" are not true dynamical variables in Chern-Simons field theory.
|
hep-th/0001170
|
Laurent Houart
|
Laurent Houart, Yolanda Lozano
|
Brane Descent Relations in M-theory
|
14 pages, LaTeX file, final version to appear in Physics Letters B
|
Phys.Lett. B479 (2000) 299-307
|
10.1016/S0370-2693(00)00317-8
|
CERN-TH/2000-025, Imperial/TP/99-0/19
|
hep-th
| null |
We discuss how the BPS branes of M-theory could be described as bound states
of non-BPS M10-branes. This conjectured M10-brane is constructed as an unstable
spacetime-filling brane in the massive eleven dimensional supergravity defined
with a Killing direction, such that 1) the BPS M9-brane is obtained after the
tachyonic mode of an M2-brane ending on it condenses, and 2) it gives the
non-BPS D9-brane of the type IIA theory upon reduction. The existence of other
non-BPS M-branes is also discussed, together with their possible stabilisation
within the Horava-Witten construction.
|
[
{
"created": "Tue, 25 Jan 2000 21:19:15 GMT",
"version": "v1"
},
{
"created": "Tue, 14 Mar 2000 12:45:53 GMT",
"version": "v2"
}
] |
2009-10-31
|
[
[
"Houart",
"Laurent",
""
],
[
"Lozano",
"Yolanda",
""
]
] |
We discuss how the BPS branes of M-theory could be described as bound states of non-BPS M10-branes. This conjectured M10-brane is constructed as an unstable spacetime-filling brane in the massive eleven dimensional supergravity defined with a Killing direction, such that 1) the BPS M9-brane is obtained after the tachyonic mode of an M2-brane ending on it condenses, and 2) it gives the non-BPS D9-brane of the type IIA theory upon reduction. The existence of other non-BPS M-branes is also discussed, together with their possible stabilisation within the Horava-Witten construction.
|
hep-th/0506205
|
Takehiro Azuma
|
Takehiro Azuma (KEK), Subrata Bal (RIKEN), Keiichi Nagao (Ibaraki U.),
Jun Nishimura (KEK & SOKENDAI)
|
Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
|
20 pages, 7 figures, (v2) some typos corrected
|
JHEP 0509 (2005) 047
|
10.1088/1126-6708/2005/09/047
|
KEK-TH-968, KUNS-1925, RIKEN-TH-39, IU-TH-2
|
hep-th hep-lat
| null |
We study a matrix model with a cubic term, which incorporates both the fuzzy
S^2*S^2 and the fuzzy S^2 as classical solutions. Both of the solutions decay
into the vacuum of the pure Yang-Mills model (even in the large-N limit) when
the coefficient of the cubic term is smaller than a critical value, but the
large-N behavior of the critical point is different for the two solutions. The
results above the critical point are nicely reproduced by the all order
calculations in perturbation theory. By comparing the free energy, we find that
the true vacuum is given either by the fuzzy S^2 or by the ``pure Yang-Mills
vacuum'' depending on the coupling constant. In Monte Carlo simulation we do
observe a decay of the fuzzy S^2*S^2 into the fuzzy S^2 at moderate N, but the
decay probability seems to be suppressed at large N. The above results,
together with our previous results for the fuzzy CP^2, reveal certain
universality in the large-N dynamics of four-dimensional fuzzy manifolds
realized in a matrix model with a cubic term.
|
[
{
"created": "Fri, 24 Jun 2005 10:01:31 GMT",
"version": "v1"
},
{
"created": "Thu, 28 Jul 2005 05:36:19 GMT",
"version": "v2"
}
] |
2009-11-11
|
[
[
"Azuma",
"Takehiro",
"",
"KEK"
],
[
"Bal",
"Subrata",
"",
"RIKEN"
],
[
"Nagao",
"Keiichi",
"",
"Ibaraki U."
],
[
"Nishimura",
"Jun",
"",
"KEK & SOKENDAI"
]
] |
We study a matrix model with a cubic term, which incorporates both the fuzzy S^2*S^2 and the fuzzy S^2 as classical solutions. Both of the solutions decay into the vacuum of the pure Yang-Mills model (even in the large-N limit) when the coefficient of the cubic term is smaller than a critical value, but the large-N behavior of the critical point is different for the two solutions. The results above the critical point are nicely reproduced by the all order calculations in perturbation theory. By comparing the free energy, we find that the true vacuum is given either by the fuzzy S^2 or by the ``pure Yang-Mills vacuum'' depending on the coupling constant. In Monte Carlo simulation we do observe a decay of the fuzzy S^2*S^2 into the fuzzy S^2 at moderate N, but the decay probability seems to be suppressed at large N. The above results, together with our previous results for the fuzzy CP^2, reveal certain universality in the large-N dynamics of four-dimensional fuzzy manifolds realized in a matrix model with a cubic term.
|
2303.18234
|
Josef Kluson
|
J. Kluson, B. Matous
|
Weyl Gravity in Covariant Hamiltonian Formalism
|
19 pages
| null | null | null |
hep-th gr-qc
|
http://creativecommons.org/publicdomain/zero/1.0/
|
We find covariant canonical formalism for Weyl invariant gravity. We discuss
constraint structure of this theory and its gauge fixed form.
|
[
{
"created": "Fri, 31 Mar 2023 17:48:31 GMT",
"version": "v1"
}
] |
2023-04-03
|
[
[
"Kluson",
"J.",
""
],
[
"Matous",
"B.",
""
]
] |
We find covariant canonical formalism for Weyl invariant gravity. We discuss constraint structure of this theory and its gauge fixed form.
|
2402.16950
|
Tom Steudtner
|
Tom Steudtner
|
Effective Potential and Vacuum Stability in the Litim-Sannino Model
|
26 pages, 7 figures; v2: extended discussion and match publication
| null | null | null |
hep-th hep-ph
|
http://creativecommons.org/licenses/by/4.0/
|
We revisit the scalar potential in the Litim-Sannino model. We compute for
the first time the full quantum corrections to the classical potential and show
that they significantly ameliorate the stability analysis at the UV fixed
point. The quantum effective potential is computed at two-loop order and the
numerical precision is further improved using resummations and parameter
optimisations. As a result, we find a consistent widening of the UV conformal
window across various approximations.
|
[
{
"created": "Mon, 26 Feb 2024 19:00:03 GMT",
"version": "v1"
},
{
"created": "Wed, 24 Apr 2024 10:48:56 GMT",
"version": "v2"
}
] |
2024-04-25
|
[
[
"Steudtner",
"Tom",
""
]
] |
We revisit the scalar potential in the Litim-Sannino model. We compute for the first time the full quantum corrections to the classical potential and show that they significantly ameliorate the stability analysis at the UV fixed point. The quantum effective potential is computed at two-loop order and the numerical precision is further improved using resummations and parameter optimisations. As a result, we find a consistent widening of the UV conformal window across various approximations.
|
hep-th/9702004
|
Julio Guerrero Garcia
|
J. Guerrero, V. Aldaya and M. Calixto
|
Algebraic Quantization on the Torus and Modular Invariance
|
Latex, 5 pages with no figures. Uses style file group21.sty
Contribution to the XXI International Colloquium on Group Theoretical Methods
in Physics, Goslar, Germany
| null | null | null |
hep-th
| null |
New features of systems with non-trivial topology such as fractional quantum
numbers, inequivalent quantizations, good operators, topological anomalies,
etc. are described in the framework of an algebraic quantization procedure on a
group. Modular invariance naturally appears as a subgroup of good operators in
the particular case of the torus.
|
[
{
"created": "Fri, 31 Jan 1997 15:45:49 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Guerrero",
"J.",
""
],
[
"Aldaya",
"V.",
""
],
[
"Calixto",
"M.",
""
]
] |
New features of systems with non-trivial topology such as fractional quantum numbers, inequivalent quantizations, good operators, topological anomalies, etc. are described in the framework of an algebraic quantization procedure on a group. Modular invariance naturally appears as a subgroup of good operators in the particular case of the torus.
|
hep-th/9410062
| null |
M.Pitk\"anen
|
p-Adic description of Higgs mechanism V: New Physics
|
37 pages,latex. Revision: correction of error in the calculation of
CKM matrix and reconsideration of top quark mass problem
| null | null | null |
hep-th
| null |
TGD suggests the existence of two new branches of physics, namely M_{89}
hadron physics and M_{127} leptohadron physics. Leptons and U type quarks are
predicted to have light colored excitations. The anomalous production of e^+e^-
pairs in heavy ion collisions sup- ports the existence of light leptomeson but
there are objections against light exotics. a) Asymptotic freedom in the
standard sense might be lost: the recently identified exotic color bosons
however save the situation. b) Z^0 decay width seems to exclude light exotics.
The solution of the problem relies on p-adic probability concept. The real
counterpart (\sum_jP(ito j))_R for the sum of p-adic probabi- lities differs
from the sum \sum_j P(i toj)_R for the real counter- parts of p-adic
probabilities. Interpretation:(\sum_jP(i to j))_R is used, when only a common
signature for final states is used. \sum_j(P(i to j)_R is used, when each final
state is monitored separately. The total decay rate of $Z^0$ to unmonitored
exotic leptons is sensitive to the value of \theta_W(eff) and vanishes for
sin^2(\theta_W(eff))=0.2324 and sensible value of \alpha_s(L)! In TGD the
observed top quark candidate most probably corresponds to u and d quarks of
M_{89} hadron physics. The details of the identification and signatures of the
new Physics are discussed.
|
[
{
"created": "Mon, 10 Oct 1994 12:46:15 GMT",
"version": "v1"
},
{
"created": "Fri, 28 Oct 1994 09:50:48 GMT",
"version": "v2"
},
{
"created": "Thu, 15 Jun 1995 08:50:33 GMT",
"version": "v3"
}
] |
2008-02-03
|
[
[
"Pitkänen",
"M.",
""
]
] |
TGD suggests the existence of two new branches of physics, namely M_{89} hadron physics and M_{127} leptohadron physics. Leptons and U type quarks are predicted to have light colored excitations. The anomalous production of e^+e^- pairs in heavy ion collisions sup- ports the existence of light leptomeson but there are objections against light exotics. a) Asymptotic freedom in the standard sense might be lost: the recently identified exotic color bosons however save the situation. b) Z^0 decay width seems to exclude light exotics. The solution of the problem relies on p-adic probability concept. The real counterpart (\sum_jP(ito j))_R for the sum of p-adic probabi- lities differs from the sum \sum_j P(i toj)_R for the real counter- parts of p-adic probabilities. Interpretation:(\sum_jP(i to j))_R is used, when only a common signature for final states is used. \sum_j(P(i to j)_R is used, when each final state is monitored separately. The total decay rate of $Z^0$ to unmonitored exotic leptons is sensitive to the value of \theta_W(eff) and vanishes for sin^2(\theta_W(eff))=0.2324 and sensible value of \alpha_s(L)! In TGD the observed top quark candidate most probably corresponds to u and d quarks of M_{89} hadron physics. The details of the identification and signatures of the new Physics are discussed.
|
hep-th/0501131
|
Xian-Hui Ge
|
Xian-Hui Ge, You-Gen Shen
|
Reconsidering the black hole final state in Dirac fields
|
7pages; Phys. Lett. B 2005 (in press)
|
Phys.Lett.B612:61-64,2005
|
10.1016/j.physletb.2005.02.050
| null |
hep-th gr-qc
| null |
We extend Horowitz and Maldacena's proposal about black hole final state to
Dirac fields and find that if annihilation of the infalling positrons and the
collapsed electrons inside the horizon is considered, then the nonlinear
evolution of collapsing quantum state will be avoided. We further propose that
annihilation also plays the central role in the process of black hole
information escaping in both Dirac and scalar fields. The computation speed of
a black hole is also briefly discussed.
|
[
{
"created": "Tue, 18 Jan 2005 06:51:29 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Ge",
"Xian-Hui",
""
],
[
"Shen",
"You-Gen",
""
]
] |
We extend Horowitz and Maldacena's proposal about black hole final state to Dirac fields and find that if annihilation of the infalling positrons and the collapsed electrons inside the horizon is considered, then the nonlinear evolution of collapsing quantum state will be avoided. We further propose that annihilation also plays the central role in the process of black hole information escaping in both Dirac and scalar fields. The computation speed of a black hole is also briefly discussed.
|
2209.07363
|
Jahed Abedi
|
Jahed Abedi
|
Firewall black holes and echoes from an action principle
|
6 pages, 3 figures. Discussion about dynamical black holes added.
Accepted for publication in Phys. Rev. D
| null |
10.1103/PhysRevD.107.064004
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
It is often said that there is no gravity theory based on local action
principles giving rise to firewall black hole solutions. Additionally, Guo and
Mathur 2022 (2205.10921) have cast doubt on the observability of firewall
echoes due to closed trapped surface produced by backreaction of macroscopic
in-falling wave packets. In this paper, we bring Einstein-Maxwell-Dilaton
action as a toy model that serves as counterexample to these assertions.
Actions with Maxwell and dilaton fields emerge from several fundamental
theories, such as the low energy limit of (super) string theory or Kaluza-Klein
compactifications. In these systems, the black hole solution has two curvature
singularities. We will show that the outer singularity inside the event horizon
can cause significant change to the outside, close to the extremal limit,
making a macroscopic reflective barrier near the event horizon that would lead
to "observable" gravitational wave echoes in this toy model. Additionally, we
also call into question the argument by Guo et al. 2017 (1711.01617) claiming
that a very small fraction of the backscattered photons will be able to escape
back to infinity from the firewall using these black holes as counterexample.
|
[
{
"created": "Thu, 15 Sep 2022 15:25:12 GMT",
"version": "v1"
},
{
"created": "Fri, 3 Mar 2023 13:35:20 GMT",
"version": "v2"
}
] |
2023-03-07
|
[
[
"Abedi",
"Jahed",
""
]
] |
It is often said that there is no gravity theory based on local action principles giving rise to firewall black hole solutions. Additionally, Guo and Mathur 2022 (2205.10921) have cast doubt on the observability of firewall echoes due to closed trapped surface produced by backreaction of macroscopic in-falling wave packets. In this paper, we bring Einstein-Maxwell-Dilaton action as a toy model that serves as counterexample to these assertions. Actions with Maxwell and dilaton fields emerge from several fundamental theories, such as the low energy limit of (super) string theory or Kaluza-Klein compactifications. In these systems, the black hole solution has two curvature singularities. We will show that the outer singularity inside the event horizon can cause significant change to the outside, close to the extremal limit, making a macroscopic reflective barrier near the event horizon that would lead to "observable" gravitational wave echoes in this toy model. Additionally, we also call into question the argument by Guo et al. 2017 (1711.01617) claiming that a very small fraction of the backscattered photons will be able to escape back to infinity from the firewall using these black holes as counterexample.
|
hep-th/0702163
|
Danilo Diaz
|
Danilo E. D\'iaz and Harald Dorn
|
Partition functions and double-trace deformations in AdS/CFT
|
18 pages, uses JHEP3.cls. Published JHEP version
|
JHEP 0705:046,2007
|
10.1088/1126-6708/2007/05/046
|
HU-EP-07/04
|
hep-th math.DG
| null |
We study the effect of a relevant double-trace deformation on the partition
function (and conformal anomaly) of a CFT at large N and its dual picture in
AdS. Three complementary previous results are brought into full agreement with
each other: bulk and boundary computations, as well as their formal identity.
We show the exact equality between the dimensionally regularized partition
functions or, equivalently, fluctuational determinants involved. A series of
results then follows: (i) equality between the renormalized partition functions
for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for
even d, the mapping entails a mixing of UV and IR effects on the same side
(bulk) of the duality, with no precedent in the leading order computations; and
finally, (iv) a subtle relation between overall coefficients, volume
renormalization and IR-UV connection. All in all, we get a clean test of the
AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and
at subleading O(1) order in the large-N expansion on the boundary.
|
[
{
"created": "Tue, 20 Feb 2007 15:58:13 GMT",
"version": "v1"
},
{
"created": "Wed, 28 Feb 2007 16:43:22 GMT",
"version": "v2"
},
{
"created": "Tue, 19 Feb 2008 11:54:12 GMT",
"version": "v3"
}
] |
2010-10-27
|
[
[
"Díaz",
"Danilo E.",
""
],
[
"Dorn",
"Harald",
""
]
] |
We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. Three complementary previous results are brought into full agreement with each other: bulk and boundary computations, as well as their formal identity. We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuational determinants involved. A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection. All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary.
|
hep-th/0010293
|
Anton Kapustin
|
Anton Kapustin, Dmitri Orlov
|
Vertex Algebras, Mirror Symmetry, And D-Branes: The Case Of Complex Tori
|
70 pages, AMS Latex. v2: a gap in the reasoning of Appendix B has
been filled, and a proof of the "Borcherds formulas" has been added
|
Comm. Math. Phys. 233 (2003), no. 1, 79--136
|
10.1007/s00220-002-0755-7
|
IASSNS-HEP-00/81
|
hep-th math.AG math.QA
| null |
A vertex algebra is an algebraic counterpart of a two-dimensional conformal
field theory. We give a new definition of a vertex algebra which includes
chiral algebras as a special case, but allows for fields which are neither
meromorphic nor anti-meromorphic. To any complex torus equipped with a flat
Kahler metric and a closed 2-form we associate an N=2 superconformal vertex
algebra (N=2 SCVA) in the sense of our definition. We find a criterion for two
different tori to produce isomorphic N=2 SCVA's. We show that for algebraic
tori isomorphism of N=2 SCVA's implies the equivalence of the derived
categories of coherent sheaves corresponding to the tori or their
noncommutative generalizations (Azumaya algebras over tori). We also find a
criterion for two different tori to produce N=2 SCVA's related by a mirror
morphism. If the 2-form is of type (1,1), this condition is identical to the
one proposed by Golyshev, Lunts, and Orlov, who used an entirely different
approach inspired by the Homological Mirror Symmetry Conjecture of Kontsevich.
Our results suggest that Kontsevich's conjecture must be modified: coherent
sheaves must be replaced with modules over Azumaya algebras, and the Fukaya
category must be ``twisted'' by a closed 2-form. We also describe the
implications of our results for BPS D-branes on Calabi-Yau manifolds.
|
[
{
"created": "Tue, 31 Oct 2000 17:47:58 GMT",
"version": "v1"
},
{
"created": "Wed, 14 Nov 2001 17:36:26 GMT",
"version": "v2"
}
] |
2009-11-24
|
[
[
"Kapustin",
"Anton",
""
],
[
"Orlov",
"Dmitri",
""
]
] |
A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor anti-meromorphic. To any complex torus equipped with a flat Kahler metric and a closed 2-form we associate an N=2 superconformal vertex algebra (N=2 SCVA) in the sense of our definition. We find a criterion for two different tori to produce isomorphic N=2 SCVA's. We show that for algebraic tori isomorphism of N=2 SCVA's implies the equivalence of the derived categories of coherent sheaves corresponding to the tori or their noncommutative generalizations (Azumaya algebras over tori). We also find a criterion for two different tori to produce N=2 SCVA's related by a mirror morphism. If the 2-form is of type (1,1), this condition is identical to the one proposed by Golyshev, Lunts, and Orlov, who used an entirely different approach inspired by the Homological Mirror Symmetry Conjecture of Kontsevich. Our results suggest that Kontsevich's conjecture must be modified: coherent sheaves must be replaced with modules over Azumaya algebras, and the Fukaya category must be ``twisted'' by a closed 2-form. We also describe the implications of our results for BPS D-branes on Calabi-Yau manifolds.
|
1012.5073
|
Winston Fairbairn
|
Winston J. Fairbairn, Karim Noui, Francesco Sardelli
|
Equivalence of the self-dual and Nambu-Goto strings
|
20 pages
| null |
10.1007/JHEP08(2011)070
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We establish explicitely the relation between the algebraic and Nambu-Goto
strings when the target space is a four dimensional flat space. We find that
the two theories are exactly equivalent only when the algebraic string is
restricted to the self-dual or anti self-dual sectors. In its Hamiltonian
formulation, the algebraic string defines a constrained system with first and
second class constraints. In the self-dual case, we exhibit the appropriate set
of second class constraints such that the resulting physical phase space is
formulated in the same way as it is in the standard Nambu-Goto string. We
conclude with a discussion on alternative quantisation schemes.
|
[
{
"created": "Wed, 22 Dec 2010 19:04:07 GMT",
"version": "v1"
}
] |
2015-05-20
|
[
[
"Fairbairn",
"Winston J.",
""
],
[
"Noui",
"Karim",
""
],
[
"Sardelli",
"Francesco",
""
]
] |
We establish explicitely the relation between the algebraic and Nambu-Goto strings when the target space is a four dimensional flat space. We find that the two theories are exactly equivalent only when the algebraic string is restricted to the self-dual or anti self-dual sectors. In its Hamiltonian formulation, the algebraic string defines a constrained system with first and second class constraints. In the self-dual case, we exhibit the appropriate set of second class constraints such that the resulting physical phase space is formulated in the same way as it is in the standard Nambu-Goto string. We conclude with a discussion on alternative quantisation schemes.
|
2207.06545
|
Jean Thierry-Mieg
|
Jean Thierry-Mieg, Peter D.Jarvis and Jerome Germoni
|
Explicit construction of the finite dimensional indecomposable
representations of the simple Lie-Kac $SU(2/1)$ superalgebra and their low
level non diagonal super Casimir operators
|
40 pages including 9 appendices giving explicitly the matrices of the
various types of representations
| null | null | null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
All finite dimensional irreducible representations of the simple Lie-Kac
super algebra SU(2/1) are explicitly constructed in the Chevalley basis as
complex matrices. For typical representations, the distinguished Dynkin label
is not quantized. We then construct the generic atypical indecomposable quivers
classified by Marcu, Su and Germoni and typical indecomposable N-generations
block triangular extensions for any irreducible module and any integer N. In
addition to the quadratic and cubic super-Casimir operators $C_2$ and $C_3$,
the supercenter of the enveloping algebra contains a chiral ghost super-Casimir
operator T of mixed order (2,4)in the odd generators, proportional to the
superidentity grading operator $\chi$, and satisfying $T = \chi\;C_2$ and we
define a new factorizable chiral-Casimir $T^-=C_2(1-\chi)/2=(UV+WX)(VU+XW)$
where (U,V,W,X) are the odd generators. In most indecomposable cases, the
super-Casimirs are non diagonal. We compute their pseudo-eigenvalues.
|
[
{
"created": "Wed, 13 Jul 2022 23:04:07 GMT",
"version": "v1"
}
] |
2022-07-15
|
[
[
"Thierry-Mieg",
"Jean",
""
],
[
"Jarvis",
"Peter D.",
""
],
[
"Germoni",
"Jerome",
""
]
] |
All finite dimensional irreducible representations of the simple Lie-Kac super algebra SU(2/1) are explicitly constructed in the Chevalley basis as complex matrices. For typical representations, the distinguished Dynkin label is not quantized. We then construct the generic atypical indecomposable quivers classified by Marcu, Su and Germoni and typical indecomposable N-generations block triangular extensions for any irreducible module and any integer N. In addition to the quadratic and cubic super-Casimir operators $C_2$ and $C_3$, the supercenter of the enveloping algebra contains a chiral ghost super-Casimir operator T of mixed order (2,4)in the odd generators, proportional to the superidentity grading operator $\chi$, and satisfying $T = \chi\;C_2$ and we define a new factorizable chiral-Casimir $T^-=C_2(1-\chi)/2=(UV+WX)(VU+XW)$ where (U,V,W,X) are the odd generators. In most indecomposable cases, the super-Casimirs are non diagonal. We compute their pseudo-eigenvalues.
|
hep-th/9807094
|
Parthasarathi Mitra
|
P. Mitra
|
Entropy of extremal black holes in asymptotically anti-de Sitter
spacetime
|
LaTeX, 9 pages; post-publication correction of sign-convention
related errors
|
Phys.Lett. B441 (1998) 89-95
|
10.1016/S0370-2693(98)01161-7
|
SINP/TNP/98-16
|
hep-th gr-qc
| null |
Unlike the extremal Reissner - Nordstr\"{o}m black hole in ordinary
spacetime, the one in anti-de Sitter spacetime is a minimum of action and has
zero entropy if quantization is carried out after extremalization. However, if
extremalization is carried out after quantization, then the entropy is a
quarter of the area as in the usual case.
|
[
{
"created": "Tue, 14 Jul 1998 09:48:10 GMT",
"version": "v1"
},
{
"created": "Thu, 16 Dec 1999 09:12:41 GMT",
"version": "v2"
}
] |
2009-10-31
|
[
[
"Mitra",
"P.",
""
]
] |
Unlike the extremal Reissner - Nordstr\"{o}m black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if quantization is carried out after extremalization. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case.
|
2003.12852
|
Roldao da Rocha
|
Roldao da Rocha
|
The minimal of geometric deformation of Yang-Mills-Dirac stellar
configurations
|
9 pages, 5 figures
|
Phys. Rev. D 102, 024011 (2020)
|
10.1103/PhysRevD.102.024011
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The method of minimal geometric deformation (MGD) is used to derive static,
strongly gravitating, spherically symmetric, compact stellar distributions that
are solutions of the Yang-Mills-Einstein-Dirac coupled field equations, on
fluid membranes with finite tension. Their solutions characterize MGD
Yang-Mills-Dirac stars, whose mass has order of the Chandrasekhar mass, once
the range of both the fermionic self-interaction and the Yang-Mills coupling
constants is suitably chosen. Physical features of MGD Yang-Mills-Dirac stars
are then discussed, and their ADM mass are derived, as a function of the
fermion coupling constant, the finite brane tension, and the Yang-Mills running
parameter as well.
|
[
{
"created": "Sat, 28 Mar 2020 17:51:01 GMT",
"version": "v1"
}
] |
2020-07-08
|
[
[
"da Rocha",
"Roldao",
""
]
] |
The method of minimal geometric deformation (MGD) is used to derive static, strongly gravitating, spherically symmetric, compact stellar distributions that are solutions of the Yang-Mills-Einstein-Dirac coupled field equations, on fluid membranes with finite tension. Their solutions characterize MGD Yang-Mills-Dirac stars, whose mass has order of the Chandrasekhar mass, once the range of both the fermionic self-interaction and the Yang-Mills coupling constants is suitably chosen. Physical features of MGD Yang-Mills-Dirac stars are then discussed, and their ADM mass are derived, as a function of the fermion coupling constant, the finite brane tension, and the Yang-Mills running parameter as well.
|
hep-th/9201019
| null |
J. A. Dixon, M. J. Duff, and E. Sezgin
|
The Coupling of Yang-Mills to Extended Objects
|
14 Pages
|
Phys.Lett.B279:265-271,1992
|
10.1016/0370-2693(92)90391-G
| null |
hep-th
| null |
The coupling of Yang-Mills fields to the heterotic string in bosonic
formulation is generalized to extended objects of higher dimension (p-branes).
For odd p, the Bianchi identities obeyed by the field strengths of the
(p+1)-forms receive Chern-Simons corrections which, in the case of the 5-brane,
are consistent with an earlier conjecture based on string/5-brane duality.
|
[
{
"created": "Fri, 10 Jan 1992 22:10:40 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Dixon",
"J. A.",
""
],
[
"Duff",
"M. J.",
""
],
[
"Sezgin",
"E.",
""
]
] |
The coupling of Yang-Mills fields to the heterotic string in bosonic formulation is generalized to extended objects of higher dimension (p-branes). For odd p, the Bianchi identities obeyed by the field strengths of the (p+1)-forms receive Chern-Simons corrections which, in the case of the 5-brane, are consistent with an earlier conjecture based on string/5-brane duality.
|
2201.07813
|
Chandramouli Chowdhury
|
Chandramouli Chowdhury, Ruchira Mishra and Siddharth G. Prabhu
|
The Asymptotic Structure of Gravity in Higher Even Dimensions
|
19 + 16 pages
| null | null | null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We investigate the notion of asymptotic symmetries in classical gravity in
higher even dimensions, with $D = 6$ space-time dimensions as the prototype.
Unlike in four dimensions, certain non-linearities persist which necessitates
the complete non-linear analysis we undertake. We show that the free data is
parametrized by a pair of symmetric trace-free tensors at future (past) null
infinity. This involves a redefinition of the radiative field. We define a
symplectic structure generating the radiative phase space at ${\cal I}^{\pm}$
with appropriate boundary conditions which are preserved by the action of
supertranslations. We derive the charge associated to super-translation vector
fields and this charge matches with that derived using the equations of motion
in the full non-linear theory. We elaborate on the precise relationship between
the super-translation charge, the Bondi mass aspect and the "gravitational
memory" in six space-time dimensions, thus providing the first example of an
infrared triangle in non-linear gravity beyond four dimensions.
|
[
{
"created": "Wed, 19 Jan 2022 19:00:49 GMT",
"version": "v1"
}
] |
2022-01-21
|
[
[
"Chowdhury",
"Chandramouli",
""
],
[
"Mishra",
"Ruchira",
""
],
[
"Prabhu",
"Siddharth G.",
""
]
] |
We investigate the notion of asymptotic symmetries in classical gravity in higher even dimensions, with $D = 6$ space-time dimensions as the prototype. Unlike in four dimensions, certain non-linearities persist which necessitates the complete non-linear analysis we undertake. We show that the free data is parametrized by a pair of symmetric trace-free tensors at future (past) null infinity. This involves a redefinition of the radiative field. We define a symplectic structure generating the radiative phase space at ${\cal I}^{\pm}$ with appropriate boundary conditions which are preserved by the action of supertranslations. We derive the charge associated to super-translation vector fields and this charge matches with that derived using the equations of motion in the full non-linear theory. We elaborate on the precise relationship between the super-translation charge, the Bondi mass aspect and the "gravitational memory" in six space-time dimensions, thus providing the first example of an infrared triangle in non-linear gravity beyond four dimensions.
|
1502.01751
|
Ying-Hsuan Lin
|
Ying-Hsuan Lin, Shu-Heng Shao, Yifan Wang, Xi Yin
|
Interpolating the Coulomb Phase of Little String Theory
|
39 pages, 4 figures, 4 tables
| null |
10.1007/JHEP12(2015)022
|
MIT-CTP/4639
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study up to 8-derivative terms in the Coulomb branch effective action of
(1,1) little string theory, by collecting results of 4-gluon scattering
amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop
order, and tree-level double scaled little string theory (DSLST). In previous
work we have matched the 6-derivative term from the 6D gauge theory to DSLST,
indicating that this term is protected on the entire Coulomb branch. The
8-derivative term, on the other hand, is unprotected. In this paper we compute
the 8-derivative term by interpolating from the two limits, near the origin and
near the infinity on the Coulomb branch, numerically from SU(k) SYM and DSLST
respectively, for k=2,3,4,5. We discuss the implication of this result on the
UV completion of 6D SYM as well as the strong coupling completion of DSLST. We
also comment on analogous interpolating functions in the Coulomb phase of
circle-compactified (2,0) little string theory.
|
[
{
"created": "Thu, 5 Feb 2015 22:38:16 GMT",
"version": "v1"
},
{
"created": "Thu, 12 Nov 2015 21:07:06 GMT",
"version": "v2"
}
] |
2016-01-27
|
[
[
"Lin",
"Ying-Hsuan",
""
],
[
"Shao",
"Shu-Heng",
""
],
[
"Wang",
"Yifan",
""
],
[
"Yin",
"Xi",
""
]
] |
We study up to 8-derivative terms in the Coulomb branch effective action of (1,1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST, indicating that this term is protected on the entire Coulomb branch. The 8-derivative term, on the other hand, is unprotected. In this paper we compute the 8-derivative term by interpolating from the two limits, near the origin and near the infinity on the Coulomb branch, numerically from SU(k) SYM and DSLST respectively, for k=2,3,4,5. We discuss the implication of this result on the UV completion of 6D SYM as well as the strong coupling completion of DSLST. We also comment on analogous interpolating functions in the Coulomb phase of circle-compactified (2,0) little string theory.
|
hep-th/0504103
|
Yoshinobu Habara
|
Yoshinobu Habara, Hikaru Kawai and Masao Ninomiya
|
Cyclic Universe \`{a} la string theory
|
Proceeding of International Workshop "Frontier of Quantum Physics"
February 17(Thu.)-19(Sat.) 2005
|
Prog.Theor.Phys.Suppl.164:7-16,2007
|
10.1143/PTPS.164.7
| null |
hep-th
| null |
We shall present a model of the "cyclic universe" that can be constructed
only by assuming a minimal set of properties of string theory. We clarify our
viewpoint of the cyclic universe and show some attempts to mateliarize the idea
as field theoretical manner.
|
[
{
"created": "Tue, 12 Apr 2005 11:07:11 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Habara",
"Yoshinobu",
""
],
[
"Kawai",
"Hikaru",
""
],
[
"Ninomiya",
"Masao",
""
]
] |
We shall present a model of the "cyclic universe" that can be constructed only by assuming a minimal set of properties of string theory. We clarify our viewpoint of the cyclic universe and show some attempts to mateliarize the idea as field theoretical manner.
|
hep-th/0007150
|
Michel Rausch
|
M. Rausch de Traubenberg
|
Fractional Supersymmetry and Lie Algebras
|
16 pages, 1 figure, LaTex file with epsf.sty, Lecture given at the
Workshop on Non Commutative Geometry and Superstring Theory, Rabat 16-17 June
2000, to appear in the proceedings
| null | null |
PM/00-20
|
hep-th math-ph math.MP math.RT
| null |
Supersymmetry and super-Lie algebras have been consistently generalized
previously. The so-called fractional supersymmetry and $F-$Lie algebras could
be constructed starting from any representation $\D$ of any Lie algebra $g$.
This involves taking the $F^{\mathrm th}$ root of $\D$ in some sense. We show,
after having constructed differential realization(s) of any Lie algebra, how
fractional supersymmetry can be explicitly realized in terms of appropriate
homogeneous monomials.
|
[
{
"created": "Wed, 19 Jul 2000 12:36:56 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"de Traubenberg",
"M. Rausch",
""
]
] |
Supersymmetry and super-Lie algebras have been consistently generalized previously. The so-called fractional supersymmetry and $F-$Lie algebras could be constructed starting from any representation $\D$ of any Lie algebra $g$. This involves taking the $F^{\mathrm th}$ root of $\D$ in some sense. We show, after having constructed differential realization(s) of any Lie algebra, how fractional supersymmetry can be explicitly realized in terms of appropriate homogeneous monomials.
|
1610.02467
|
Takahiro Kubota
|
Allan L. Alinea, Takahiro Kubota and Nobuhiko Misumi
|
The double-soft limit in cosmological correlation functions and graviton
exchange effects
|
14 pages, 1 figure, references added
|
JCAP 01 (2017) 034
|
10.1088/1475-7516/2017/01/034
|
OU-HET 907
|
hep-th astro-ph.CO
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The graviton exchange effect on cosmological correlation functions is
examined by employing the double-soft limit technique. A new relation among
correlation functions that contain the effects due to graviton exchange
diagrams in addition to those due to scalar-exchange and
scalar-contact-interaction, is derived by using the background field method and
independently by the method of Ward identities associated with dilatation
symmetry. We compare these three terms, putting small values for the slow-roll
parameters and $(1-n_{s}) = 0.042$, where $n_{s}$ is the scalar spectral index.
It is argued that the graviton exchange effects are more dominant than the
other two and could be observed in the trispectrum in the double-soft limit.
Our observation strengthens the previous work by Seery, Sloth and Vernizzi, in
which it has been argued that the graviton exchange dominates in the
counter-collinear limit for single field slow-roll inflation.
|
[
{
"created": "Sat, 8 Oct 2016 03:00:14 GMT",
"version": "v1"
},
{
"created": "Mon, 17 Oct 2016 01:32:43 GMT",
"version": "v2"
},
{
"created": "Sun, 4 Dec 2016 15:13:28 GMT",
"version": "v3"
}
] |
2017-01-26
|
[
[
"Alinea",
"Allan L.",
""
],
[
"Kubota",
"Takahiro",
""
],
[
"Misumi",
"Nobuhiko",
""
]
] |
The graviton exchange effect on cosmological correlation functions is examined by employing the double-soft limit technique. A new relation among correlation functions that contain the effects due to graviton exchange diagrams in addition to those due to scalar-exchange and scalar-contact-interaction, is derived by using the background field method and independently by the method of Ward identities associated with dilatation symmetry. We compare these three terms, putting small values for the slow-roll parameters and $(1-n_{s}) = 0.042$, where $n_{s}$ is the scalar spectral index. It is argued that the graviton exchange effects are more dominant than the other two and could be observed in the trispectrum in the double-soft limit. Our observation strengthens the previous work by Seery, Sloth and Vernizzi, in which it has been argued that the graviton exchange dominates in the counter-collinear limit for single field slow-roll inflation.
|
hep-th/0112007
|
A. D. Alhaidari
|
A. D. Alhaidari
|
Relativistic shape invariant potentials
|
Corrigendum: The last statement above equation (1) is now corrected
and replaced by two new statements
|
J.Phys.A34:9827,2002; Erratum-ibid.35:6207,2002
|
10.1088/0305-4470/34/46/306
| null |
hep-th
| null |
Dirac equation for a charged spinor in electromagnetic field is written for
special cases of spherically symmetric potentials. This facilitates the
introduction of relativistic extensions of shape invariant potential classes.
We obtain the relativistic spectra and spinor wavefunctions for all potentials
in one of these classes. The nonrelativistic limit reproduces the usual
Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.
|
[
{
"created": "Sun, 2 Dec 2001 18:54:17 GMT",
"version": "v1"
},
{
"created": "Fri, 14 Dec 2001 10:21:14 GMT",
"version": "v2"
},
{
"created": "Tue, 5 Mar 2002 19:54:32 GMT",
"version": "v3"
}
] |
2008-11-26
|
[
[
"Alhaidari",
"A. D.",
""
]
] |
Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.
|
1306.0220
|
Georgios Linardopoulos
|
Minos Axenides, Emmanuel Floratos and Georgios Linardopoulos
|
Stringy Membranes in AdS/CFT
|
40 pages, 9 figures; published version
|
JHEP 08 (2013) 089
|
10.1007/JHEP08(2013)089
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study membrane configurations in AdS_{7/4}xS^{4/7}. The membranes are
wrapped around the compact manifold S^{4/7} and are dynamically equivalent to
bosonic strings in AdS_5. We thus conveniently identify them as "Stringy
Membranes". For the case of AdS_7xS^4, their construction is carried out by
embedding the Polyakov action for classical bosonic strings in AdS_5, into the
corresponding membrane action. Therefore, every string configuration in AdS_5
can be realized by an appropriately chosen stringy membrane in AdS_7xS^4. We
discuss the possibility of this being also the case for stringy membranes in
AdS_4xS^7/Z^k (k > 1 or k = 1). By performing a stability analysis to the
constructed solutions, we find that the (membrane) fluctuations along their
transverse directions are organized in multiple Lam\'{e} stability bands and
gaps in the space of parameters of the configurations. In this membrane
picture, strings exhibit a single band/gap structure.
|
[
{
"created": "Sun, 2 Jun 2013 15:51:37 GMT",
"version": "v1"
},
{
"created": "Tue, 17 Sep 2013 17:08:24 GMT",
"version": "v2"
}
] |
2021-05-27
|
[
[
"Axenides",
"Minos",
""
],
[
"Floratos",
"Emmanuel",
""
],
[
"Linardopoulos",
"Georgios",
""
]
] |
We study membrane configurations in AdS_{7/4}xS^{4/7}. The membranes are wrapped around the compact manifold S^{4/7} and are dynamically equivalent to bosonic strings in AdS_5. We thus conveniently identify them as "Stringy Membranes". For the case of AdS_7xS^4, their construction is carried out by embedding the Polyakov action for classical bosonic strings in AdS_5, into the corresponding membrane action. Therefore, every string configuration in AdS_5 can be realized by an appropriately chosen stringy membrane in AdS_7xS^4. We discuss the possibility of this being also the case for stringy membranes in AdS_4xS^7/Z^k (k > 1 or k = 1). By performing a stability analysis to the constructed solutions, we find that the (membrane) fluctuations along their transverse directions are organized in multiple Lam\'{e} stability bands and gaps in the space of parameters of the configurations. In this membrane picture, strings exhibit a single band/gap structure.
|
2209.09215
|
Henrique Matheus Gauy
|
Henrique Matheus Gauy, Alex E. Bernardini
|
Gravity Localization on Intersecting Thick Braneworlds
|
19 pages, 5 figures. To be published in Physical Review D,
https://journals.aps.org/prd/accepted/33079Q52D301eb3a40da34b6972dcbce54b13d2dc
| null | null | null |
hep-th gr-qc
|
http://creativecommons.org/licenses/by/4.0/
|
The localization of gravity for (5 + 1)-dimensional intersecting thick
braneworld models is thoroughly investigated. Departing from preliminary
results for five independent proposals, from I to V, gravity is shown to be
localized in the brane. In particular, for models from I to III, only the zero
modes are analytically determined. On the other hand, for models IV and V,
massive modes are all obtained: a finite number of massive states is identified
for model IV, while an infinite but discrete number of massive states bounded
from below is exhibited by model V. Considering that the discreteness of the
graviton modes implies that gravity does not propagate in the co-dimensions,
the naked singularities of models IV and V, at edges of space, are made
harmless. To conclude, the phenomenological implications for sphere models,
constructed out of models III and IV, are also discussed. According to such an
overall classification, if the internal space is a sphere, model IV is shown to
exhibit normalizable modes. More relevantly, for the sphere model assembled out
of model III, the subtle property of reproducing a consistent Newtonian limit
is identified.
|
[
{
"created": "Mon, 19 Sep 2022 17:29:58 GMT",
"version": "v1"
}
] |
2022-09-20
|
[
[
"Gauy",
"Henrique Matheus",
""
],
[
"Bernardini",
"Alex E.",
""
]
] |
The localization of gravity for (5 + 1)-dimensional intersecting thick braneworld models is thoroughly investigated. Departing from preliminary results for five independent proposals, from I to V, gravity is shown to be localized in the brane. In particular, for models from I to III, only the zero modes are analytically determined. On the other hand, for models IV and V, massive modes are all obtained: a finite number of massive states is identified for model IV, while an infinite but discrete number of massive states bounded from below is exhibited by model V. Considering that the discreteness of the graviton modes implies that gravity does not propagate in the co-dimensions, the naked singularities of models IV and V, at edges of space, are made harmless. To conclude, the phenomenological implications for sphere models, constructed out of models III and IV, are also discussed. According to such an overall classification, if the internal space is a sphere, model IV is shown to exhibit normalizable modes. More relevantly, for the sphere model assembled out of model III, the subtle property of reproducing a consistent Newtonian limit is identified.
|
hep-th/0309103
|
Markus A. Luty
|
Hock-Seng Goh, Markus A. Luty, Siew-Phang Ng
|
Supersymmetry without Supersymmetry
|
24 pages, LaTeX2e, no figures
|
JHEP 0501:040,2005
|
10.1088/1126-6708/2005/01/040
|
UMD-PP-03-70
|
hep-th hep-ph
| null |
We investigate the possibility that supersymmetry is not a fundamental
symmetry of nature, but emerges as an accidental approximate global symmetry at
low energies. This can occur if the visible sector is non-supersymmetric at
high scales, but flows toward a strongly-coupled superconformal fixed point at
low energies; or, alternatively, if the visible sector is localized near the
infrared brane of a warped higher-dimensional spacetime with supersymmetry
broken only on the UV brane. These two scenarios are related by the AdS/CFT
correspondence. In order for supersymmetry to solve the hierarchy problem, the
conformal symmetry must be broken below 10^{11} GeV. Accelerated unification
can naturally explain the observed gauge coupling unification by physics below
the conformal breaking scale. In this framework, there is no gravitino and no
reason for the existence of gravitational moduli, thus eliminating the
cosmological problems associated with these particles. No special dynamics is
required to break supersymmetry; rather, supersymmetry is broken at observable
energies because the fixed point is never reached. In 4D language, this can be
due to irrelevant supersymmetry breaking operators with approximately equal
dimensions. In 5D language, the size of the extra dimension is stabilized by
massive bulk fields. No small input parameters are required to generate a large
hierarchy. Supersymmetry can be broken in the visible sector either through
direct mediation or by the F term of the modulus associated with the breaking
of conformal invariance.
|
[
{
"created": "Wed, 10 Sep 2003 14:38:28 GMT",
"version": "v1"
}
] |
2010-02-03
|
[
[
"Goh",
"Hock-Seng",
""
],
[
"Luty",
"Markus A.",
""
],
[
"Ng",
"Siew-Phang",
""
]
] |
We investigate the possibility that supersymmetry is not a fundamental symmetry of nature, but emerges as an accidental approximate global symmetry at low energies. This can occur if the visible sector is non-supersymmetric at high scales, but flows toward a strongly-coupled superconformal fixed point at low energies; or, alternatively, if the visible sector is localized near the infrared brane of a warped higher-dimensional spacetime with supersymmetry broken only on the UV brane. These two scenarios are related by the AdS/CFT correspondence. In order for supersymmetry to solve the hierarchy problem, the conformal symmetry must be broken below 10^{11} GeV. Accelerated unification can naturally explain the observed gauge coupling unification by physics below the conformal breaking scale. In this framework, there is no gravitino and no reason for the existence of gravitational moduli, thus eliminating the cosmological problems associated with these particles. No special dynamics is required to break supersymmetry; rather, supersymmetry is broken at observable energies because the fixed point is never reached. In 4D language, this can be due to irrelevant supersymmetry breaking operators with approximately equal dimensions. In 5D language, the size of the extra dimension is stabilized by massive bulk fields. No small input parameters are required to generate a large hierarchy. Supersymmetry can be broken in the visible sector either through direct mediation or by the F term of the modulus associated with the breaking of conformal invariance.
|
hep-th/9802081
|
Yu-Ping Kuang
|
Kun Shen and Yu-Ping Kuang
|
Ward-Takahashi Identity and Dynamical Mass Generation in Abelian Gauge
Theories
|
15 pages RevTex with 4 figures using epsfig.sty, to appear in Phys.
Rev. D
|
Phys.Rev. D57 (1998) 6386-6397
|
10.1103/PhysRevD.57.6386
|
TUIMP-TH-97/93
|
hep-th
| null |
We derive Ward-Takahashi identities including composite fields in Abelian
gauge theories and the matching condition between the elementary field
description and the composite field description. With these we develop an
approach to dynamical symmetry breaking in Abelian gauge theories including the
study of the dynamically generated masses of the gauge boson, the fermions and
the composite Higgs field. The Cornwall-Norton, Jackiw-Johnson and Schwinger
models are taken as examples of the application. The obtained gauge boson
masses are in agreement with the existing results. In this appraoch, we are
able to further obtain new results for the mass of the composite Higgs boson
and the goldstone boson decay constant.
|
[
{
"created": "Thu, 12 Feb 1998 10:10:22 GMT",
"version": "v1"
}
] |
2009-10-31
|
[
[
"Shen",
"Kun",
""
],
[
"Kuang",
"Yu-Ping",
""
]
] |
We derive Ward-Takahashi identities including composite fields in Abelian gauge theories and the matching condition between the elementary field description and the composite field description. With these we develop an approach to dynamical symmetry breaking in Abelian gauge theories including the study of the dynamically generated masses of the gauge boson, the fermions and the composite Higgs field. The Cornwall-Norton, Jackiw-Johnson and Schwinger models are taken as examples of the application. The obtained gauge boson masses are in agreement with the existing results. In this appraoch, we are able to further obtain new results for the mass of the composite Higgs boson and the goldstone boson decay constant.
|
2203.17157
|
Nadav Drukker
|
Nadav Drukker, Ziwen Kong and Georgios Sakkas
|
Broken global symmetries and defect conformal manifolds
|
v1: 19 pages; v2: Scope of paper broadened a bit and title changed to
reflect that. Added the case of ABJM and shortened to 7 pages (2-column).
Version to appear in PRL
| null |
10.1103/PhysRevLett.129.201603
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Just as exactly marginal operators allow to deform a conformal field theory
along the space of theories known as the conformal manifold, appropriate
operators on conformal defects allow for deformations of the defects. When a
defect breaks a global symmetry, there is a contact term in the conservation
equation with an exactly marginal defect operator. The resulting defect
conformal manifold is the symmetry breaking coset and its Zamolodchikov metric
is expressed as the 2-point function of the exactly marginal operator. As the
Riemann tensor on the conformal manifold can be expressed as an integrated
4-point function of the marginal operators, we find an exact relation to the
curvature of the coset space. We confirm this relation against previously
obtained 4-point functions for insertions into the 1/2 BPS Wilson loop in
${\cal N} = 4$ SYM and 3d ${\cal N} = 6$ theory and the 1/2 BPS surface
operator of the 6d ${\cal N} = (2, 0)$ theory.
|
[
{
"created": "Thu, 31 Mar 2022 16:29:33 GMT",
"version": "v1"
},
{
"created": "Tue, 18 Oct 2022 17:24:54 GMT",
"version": "v2"
}
] |
2022-11-23
|
[
[
"Drukker",
"Nadav",
""
],
[
"Kong",
"Ziwen",
""
],
[
"Sakkas",
"Georgios",
""
]
] |
Just as exactly marginal operators allow to deform a conformal field theory along the space of theories known as the conformal manifold, appropriate operators on conformal defects allow for deformations of the defects. When a defect breaks a global symmetry, there is a contact term in the conservation equation with an exactly marginal defect operator. The resulting defect conformal manifold is the symmetry breaking coset and its Zamolodchikov metric is expressed as the 2-point function of the exactly marginal operator. As the Riemann tensor on the conformal manifold can be expressed as an integrated 4-point function of the marginal operators, we find an exact relation to the curvature of the coset space. We confirm this relation against previously obtained 4-point functions for insertions into the 1/2 BPS Wilson loop in ${\cal N} = 4$ SYM and 3d ${\cal N} = 6$ theory and the 1/2 BPS surface operator of the 6d ${\cal N} = (2, 0)$ theory.
|
hep-th/0701187
|
Bill Spence
|
Andreas Brandhuber, Simon McNamara, Bill Spence and Gabriele
Travaglini
|
Recursion Relations for One-Loop Gravity Amplitudes
|
28 pages, LaTeX, 12 figures. v2:typos and references corrected
|
JHEP 0703:029,2007
|
10.1088/1126-6708/2007/03/029
|
QMUL-PH-07-02
|
hep-th
| null |
We study the application of recursion relations to the calculation of finite
one-loop gravity amplitudes. It is shown explicitly that the known four, five,
and six graviton one-loop amplitudes for which the external legs have identical
outgoing helicities, and the four graviton amplitude with helicities (-,+,+,+)
can be derived from simple recursion relations. The latter amplitude is derived
by introducing a one-loop three-point vertex of gravitons of positive helicity,
which is the counterpart in gravity of the one-loop three-plus vertex in
Yang-Mills. We show that new issues arise for the five point amplitude with
helicities (-,+,+,+,+), where the application of known methods does not appear
to work, and we discuss possible resolutions.
|
[
{
"created": "Fri, 19 Jan 2007 18:47:29 GMT",
"version": "v1"
},
{
"created": "Tue, 30 Jan 2007 14:08:02 GMT",
"version": "v2"
}
] |
2010-10-27
|
[
[
"Brandhuber",
"Andreas",
""
],
[
"McNamara",
"Simon",
""
],
[
"Spence",
"Bill",
""
],
[
"Travaglini",
"Gabriele",
""
]
] |
We study the application of recursion relations to the calculation of finite one-loop gravity amplitudes. It is shown explicitly that the known four, five, and six graviton one-loop amplitudes for which the external legs have identical outgoing helicities, and the four graviton amplitude with helicities (-,+,+,+) can be derived from simple recursion relations. The latter amplitude is derived by introducing a one-loop three-point vertex of gravitons of positive helicity, which is the counterpart in gravity of the one-loop three-plus vertex in Yang-Mills. We show that new issues arise for the five point amplitude with helicities (-,+,+,+,+), where the application of known methods does not appear to work, and we discuss possible resolutions.
|
1807.11522
|
Mao Zeng
|
Samuel Abreu, Ben Page, Mao Zeng
|
Differential equations from unitarity cuts: nonplanar hexa-box integrals
|
31 pages, 2 figures. Version 2: final journal version; includes
solutions to differential equations
|
JHEP 01 (2019) 006
|
10.1007/JHEP01(2019)006
|
FR-PHENO-2018-009, UCLA/18/TEP/105
|
hep-th hep-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We compute $\epsilon$-factorized differential equations for all
dimensionally-regularized integrals of the nonplanar hexa-box topology, which
contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure
integrals is presented. For 5-point planar topologies, Gram determinants which
vanish in $4$ dimensions are used to build compact expressions for pure
integrals. Using unitarity cuts and computational algebraic geometry, we obtain
a compact IBP system which can be solved in 8 hours on a single CPU core,
overcoming a major bottleneck for deriving the differential equations.
Alternatively, assuming prior knowledge of the alphabet of the nonplanar
hexa-box, we reconstruct analytic differential equations from 30 numerical
phase-space points, making the computation almost trivial with current
techniques. We solve the differential equations to obtain the values of the
master integrals at the symbol level. Full results for the differential
equations and solutions are included as supplementary material.
|
[
{
"created": "Mon, 30 Jul 2018 18:37:03 GMT",
"version": "v1"
},
{
"created": "Wed, 2 Jan 2019 23:52:11 GMT",
"version": "v2"
}
] |
2019-01-04
|
[
[
"Abreu",
"Samuel",
""
],
[
"Page",
"Ben",
""
],
[
"Zeng",
"Mao",
""
]
] |
We compute $\epsilon$-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is presented. For 5-point planar topologies, Gram determinants which vanish in $4$ dimensions are used to build compact expressions for pure integrals. Using unitarity cuts and computational algebraic geometry, we obtain a compact IBP system which can be solved in 8 hours on a single CPU core, overcoming a major bottleneck for deriving the differential equations. Alternatively, assuming prior knowledge of the alphabet of the nonplanar hexa-box, we reconstruct analytic differential equations from 30 numerical phase-space points, making the computation almost trivial with current techniques. We solve the differential equations to obtain the values of the master integrals at the symbol level. Full results for the differential equations and solutions are included as supplementary material.
|
1412.1090
|
Mukund Rangamani
|
Felix M. Haehl, R. Loganayagam, Mukund Rangamani
|
The eightfold way to dissipation
|
5 pages, 1 figure. v2: minor clarifications. v3: minor changes. title
in published version differs
|
Phys. Rev. Lett. 114, 201601 (2015)
|
10.1103/PhysRevLett.114.201601
|
DCPT-14/65
|
hep-th cond-mat.stat-mech gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We provide a complete characterization of hydrodynamic transport consistent
with the second law of thermodynamics at arbitrary orders in the gradient
expansion. A key ingredient in facilitating this analysis is the notion of
adiabatic hydrodynamics, which enables isolation of the genuinely dissipative
parts of transport. We demonstrate that most transport is adiabatic.
Furthermore, of the dissipative part, only terms at the leading order in
gradient expansion are constrained to be sign-definite by the second law (as
has been derived before).
|
[
{
"created": "Tue, 2 Dec 2014 21:00:07 GMT",
"version": "v1"
},
{
"created": "Mon, 8 Dec 2014 17:50:00 GMT",
"version": "v2"
},
{
"created": "Tue, 5 May 2015 10:57:16 GMT",
"version": "v3"
}
] |
2015-05-27
|
[
[
"Haehl",
"Felix M.",
""
],
[
"Loganayagam",
"R.",
""
],
[
"Rangamani",
"Mukund",
""
]
] |
We provide a complete characterization of hydrodynamic transport consistent with the second law of thermodynamics at arbitrary orders in the gradient expansion. A key ingredient in facilitating this analysis is the notion of adiabatic hydrodynamics, which enables isolation of the genuinely dissipative parts of transport. We demonstrate that most transport is adiabatic. Furthermore, of the dissipative part, only terms at the leading order in gradient expansion are constrained to be sign-definite by the second law (as has been derived before).
|
2204.07440
|
Yui Hayashi
|
Yui Hayashi and Yuya Tanizaki
|
Non-invertible self-duality defects of Cardy-Rabinovici model and mixed
gravitational anomaly
|
53 pages, 3 figures. v2: corrections to the fusion rules, references
added
|
JHEP 08 (2022) 036
|
10.1007/JHEP08(2022)036
|
YITP-22-12
|
hep-th cond-mat.str-el hep-lat
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study properties of self-duality symmetry in the Cardy-Rabinovici model.
The Cardy-Rabinovici model is the $4$d $U(1)$ gauge theory with electric and
magnetic matters, and it enjoys the $SL(2,\mathbb{Z})$ self-duality at
low-energies. $SL(2,\mathbb{Z})$ self-duality does not realize in a naive way,
but we notice that the $ST^{p}$ duality transformation becomes the legitimate
duality operation by performing the gauging of $\mathbb{Z}_N$ $1$-form symmetry
with including the level-$p$ discrete topological term. Due to such
complications in its realization, the fusion rule of duality defects becomes a
non-group-like structure, and thus the self-duality symmetry is realized as a
non-invertible symmetry. Moreover, for some fixed points of the self-duality,
the duality symmetry turns out to have a mixed gravitational anomaly detected
on a $K3$ surface, and we can rule out the trivially gapped phase as a
consequence of anomaly matching. We also uncover how the conjectured phase
diagram of the Cardy-Rabinovici model satisfies this new anomaly matching
condition.
|
[
{
"created": "Fri, 15 Apr 2022 12:31:46 GMT",
"version": "v1"
},
{
"created": "Mon, 13 Jun 2022 17:41:44 GMT",
"version": "v2"
}
] |
2022-08-05
|
[
[
"Hayashi",
"Yui",
""
],
[
"Tanizaki",
"Yuya",
""
]
] |
We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the $4$d $U(1)$ gauge theory with electric and magnetic matters, and it enjoys the $SL(2,\mathbb{Z})$ self-duality at low-energies. $SL(2,\mathbb{Z})$ self-duality does not realize in a naive way, but we notice that the $ST^{p}$ duality transformation becomes the legitimate duality operation by performing the gauging of $\mathbb{Z}_N$ $1$-form symmetry with including the level-$p$ discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a $K3$ surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.
|
hep-th/9911142
|
Marianne Rooman
|
M. Rooman, Ph. Spindel
|
Aspects of (2+1) dimensional gravity: AdS3 asymptotic dynamics in the
framework of Fefferman-Graham-Lee theorems
|
6 pages, Latex, presented at the Journees Relativistes 99, Weimar,
September 12-17, 1999; revised version with minor modifications and 1
reference added
|
Annalen Phys. 9 (2000) 161-167
| null |
ULB-TH/99-29; UMH-MG/99-06
|
hep-th
| null |
Using the Chern-Simon formulation of (2+1) gravity, we derive, for the
general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the
emergence of the Liouville mode associated to the boundary degrees of freedom
of (2+1) dimensional anti de Sitter geometries.
|
[
{
"created": "Thu, 18 Nov 1999 14:56:48 GMT",
"version": "v1"
},
{
"created": "Thu, 2 Dec 1999 12:04:54 GMT",
"version": "v2"
}
] |
2007-05-23
|
[
[
"Rooman",
"M.",
""
],
[
"Spindel",
"Ph.",
""
]
] |
Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de Sitter geometries.
|
0801.4907
|
Igor Samsonov
|
I.L. Buchbinder, I.B. Samsonov
|
N=3 Superparticle Model
|
1+31 pages; minor mistakes are corrected, reference added, published
version
|
Nucl.Phys.B802:180-207,2008
|
10.1016/j.nuclphysb.2008.05.014
| null |
hep-th
| null |
We consider the formulation and quantization of the N=3 superparticle model,
both with and without central charge. Without the central charge the action
possesses U(3) invariance and therefore is naturally quantized in the N=3
harmonic superspace. The quantization reproduces the N=3 supergauge strength
multiplets, described by analytic N=3 superfields and a gravitino multiplet as
a constrained N=3 chiral superfield. When the central charge is present, it
breaks the U(3) R-symmetry of N=3 superalgebra down to SU(2)xU(1), and the
corresponding superparticle model is formulated in the N=2 harmonic superspace
extended by a pair of extra Grassmann variables. The quantization of such a
model leads to the massive BPS N=3 vector multiplet. It is shown that upon
additional superfield constraints such multiplet reduces to the massive N=2
vector multiplet.
|
[
{
"created": "Thu, 31 Jan 2008 15:59:38 GMT",
"version": "v1"
},
{
"created": "Tue, 12 Feb 2008 12:14:30 GMT",
"version": "v2"
},
{
"created": "Sat, 24 May 2008 13:48:04 GMT",
"version": "v3"
},
{
"created": "Wed, 4 Jun 2008 14:58:23 GMT",
"version": "v4"
}
] |
2008-11-26
|
[
[
"Buchbinder",
"I. L.",
""
],
[
"Samsonov",
"I. B.",
""
]
] |
We consider the formulation and quantization of the N=3 superparticle model, both with and without central charge. Without the central charge the action possesses U(3) invariance and therefore is naturally quantized in the N=3 harmonic superspace. The quantization reproduces the N=3 supergauge strength multiplets, described by analytic N=3 superfields and a gravitino multiplet as a constrained N=3 chiral superfield. When the central charge is present, it breaks the U(3) R-symmetry of N=3 superalgebra down to SU(2)xU(1), and the corresponding superparticle model is formulated in the N=2 harmonic superspace extended by a pair of extra Grassmann variables. The quantization of such a model leads to the massive BPS N=3 vector multiplet. It is shown that upon additional superfield constraints such multiplet reduces to the massive N=2 vector multiplet.
|
hep-th/9907131
|
Suresh Govindarajan
|
Suresh Govindarajan (IITM), T. Jayaraman (IMSc) and Tapobrata Sarkar
(IMSc)
|
Worldsheet approaches to D-branes on supersymmetric cycles
|
28 pages, LaTeX with revtex; (v2) Condition involving superpotential
in the boundary LG model imposed, references included ; (v3) final version to
appear in journal
|
Nucl.Phys. B580 (2000) 519-547
|
10.1016/S0550-3213(00)00140-1
|
IMSc 99/07/25
|
hep-th
| null |
We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau
manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as
well as by consideration of boundary states in the corresponding Gepner models.
The Landau-Ginzburg approach enables us to provide a target space
interpretation for the boundary states. The boundary states are obtained by
applying Cardy's procedure to combinations of characters in the Gepner models
which are invariant under spectral flow. We are able to relate the two
descriptions using the common discrete symmetries of the two descriptions. We
are thus able to provide an extension to the boundary of the bulk
correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner
models.
|
[
{
"created": "Thu, 15 Jul 1999 16:52:43 GMT",
"version": "v1"
},
{
"created": "Tue, 7 Sep 1999 05:56:40 GMT",
"version": "v2"
},
{
"created": "Tue, 28 Mar 2000 09:49:27 GMT",
"version": "v3"
}
] |
2009-10-31
|
[
[
"Govindarajan",
"Suresh",
"",
"IITM"
],
[
"Jayaraman",
"T.",
"",
"IMSc"
],
[
"Sarkar",
"Tapobrata",
"",
"IMSc"
]
] |
We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau-Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy's procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using the common discrete symmetries of the two descriptions. We are thus able to provide an extension to the boundary of the bulk correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner models.
|
2106.10890
|
Andrzej Sitarz
|
Arkadiusz Bochniak, Pawe{\l} Zalecki, Andrzej Sitarz
|
Spectral action and the electroweak $\theta$-terms for the Standard
Model without fermion doubling
|
26 pages
|
JHEP 12 (2021) 142
|
10.1007/JHEP12(2021)142
| null |
hep-th math-ph math.MP math.QA
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We compute the leading terms of the spectral action for a noncommutative
geometry model that has no fermion doubling. The spectral triple describing it,
which is chiral and allows for CP-symmetry breaking, has the Dirac operator
that is not of the product type. Using Wick rotation we derive explicitly the
Lagrangian of the model from the spectral action for a flat metric,
demonstrating the appearance of the topological $\theta$-terms for the
electroweak gauge fields.
|
[
{
"created": "Mon, 21 Jun 2021 07:08:49 GMT",
"version": "v1"
},
{
"created": "Tue, 22 Jun 2021 06:13:28 GMT",
"version": "v2"
},
{
"created": "Tue, 11 Jan 2022 09:07:21 GMT",
"version": "v3"
}
] |
2022-10-19
|
[
[
"Bochniak",
"Arkadiusz",
""
],
[
"Zalecki",
"Paweł",
""
],
[
"Sitarz",
"Andrzej",
""
]
] |
We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not of the product type. Using Wick rotation we derive explicitly the Lagrangian of the model from the spectral action for a flat metric, demonstrating the appearance of the topological $\theta$-terms for the electroweak gauge fields.
|
hep-th/9609077
|
Yoshihisa Kitazawa
|
Toshiaki Aida and Yoshihisa Kitazawa
|
Two-loop Prediction for Scaling Exponents in (2 + \epsilon)-dimensional
Quantum Gravity
|
36 pages, Latex file, 6 figures
|
Nucl.Phys. B491 (1997) 427-460
|
10.1016/S0550-3213(97)00091-6
|
TIT-HEP-343
|
hep-th
| null |
We perform the two loop level renormalization of quantum gravity in
$2+\epsilon$ dimensions. We work in the background gauge whose manifest
covariance enables us to use the short distance expansion of the Green's
functions. We explicitly show that the theory is renormalizable to the two loop
level in our formalism. We further make a physical prediction for the scaling
relation between the gravitational coupling constant and the cosmological
constant which is expected to hold at the short distance fixed point of the
renormalization group. It is found that the two loop level calculation is
necessary to determine the scaling exponent to the leading order in $\epsilon$.
|
[
{
"created": "Tue, 10 Sep 1996 08:33:22 GMT",
"version": "v1"
}
] |
2009-10-30
|
[
[
"Aida",
"Toshiaki",
""
],
[
"Kitazawa",
"Yoshihisa",
""
]
] |
We perform the two loop level renormalization of quantum gravity in $2+\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly show that the theory is renormalizable to the two loop level in our formalism. We further make a physical prediction for the scaling relation between the gravitational coupling constant and the cosmological constant which is expected to hold at the short distance fixed point of the renormalization group. It is found that the two loop level calculation is necessary to determine the scaling exponent to the leading order in $\epsilon$.
|
2011.05337
|
Lars Aalsma
|
Lars Aalsma, Alex Cole, Gregory J. Loges, Gary Shiu
|
A New Spin on the Weak Gravity Conjecture
|
29 pages + appendices, 4 figures. v2: added references, introduced
total landscaping principle
| null |
10.1007/JHEP03(2021)085
| null |
hep-th hep-ph
|
http://creativecommons.org/licenses/by/4.0/
|
The mild form of the Weak Gravity Conjecture states that quantum or
higher-derivative corrections should decrease the mass of large extremal
charged black holes at fixed charge. This allows extremal black holes to decay,
unless protected by a symmetry (such as supersymmetry). We reformulate this
conjecture as an integrated condition on the effective stress tensor capturing
the effect of quantum or higher-derivative corrections. In addition to charged
black holes, we also consider rotating BTZ black holes and show that this
condition is satisfied as a consequence of the $c$-theorem, proving a spinning
version of the Weak Gravity Conjecture. We also apply our results to a
five-dimensional boosted black string with higher-derivative corrections. The
boosted black string has a $\text{BTZ}\times S^2$ near-horizon geometry and,
after Kaluza-Klein reduction, describes a four-dimensional charged black hole.
Combining the spinning and charged Weak Gravity Conjecture we obtain positivity
bounds on the five-dimensional Wilson coefficients that are stronger than those
obtained from charged black holes alone.
|
[
{
"created": "Tue, 10 Nov 2020 19:00:01 GMT",
"version": "v1"
},
{
"created": "Mon, 26 Apr 2021 14:27:45 GMT",
"version": "v2"
}
] |
2021-04-27
|
[
[
"Aalsma",
"Lars",
""
],
[
"Cole",
"Alex",
""
],
[
"Loges",
"Gregory J.",
""
],
[
"Shiu",
"Gary",
""
]
] |
The mild form of the Weak Gravity Conjecture states that quantum or higher-derivative corrections should decrease the mass of large extremal charged black holes at fixed charge. This allows extremal black holes to decay, unless protected by a symmetry (such as supersymmetry). We reformulate this conjecture as an integrated condition on the effective stress tensor capturing the effect of quantum or higher-derivative corrections. In addition to charged black holes, we also consider rotating BTZ black holes and show that this condition is satisfied as a consequence of the $c$-theorem, proving a spinning version of the Weak Gravity Conjecture. We also apply our results to a five-dimensional boosted black string with higher-derivative corrections. The boosted black string has a $\text{BTZ}\times S^2$ near-horizon geometry and, after Kaluza-Klein reduction, describes a four-dimensional charged black hole. Combining the spinning and charged Weak Gravity Conjecture we obtain positivity bounds on the five-dimensional Wilson coefficients that are stronger than those obtained from charged black holes alone.
|
1502.03281
|
Mohammad Naghdi
|
M. Naghdi
|
Dual Localized Objects From M-Branes Over AdS_4 x S^7/Z_k
|
20 pages, than the v2 version: minor changes, some discussions
improved, references added and typos fixed
|
Class. Quantum Grav. 32, 215018 (2015)
|
10.1088/0264-9381/32/21/215018
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We consider a few ansatzs for the four and seven forms of 11-dimensional
supergravity over AdS_4 x S^7/Z_k while try to keep the geometry unchanged.
From the 4-form equations, we arrive at some massless scalars and pseudoscalars
in the bulk of Euclidean AdS_4 that match with some boundary $\Delta_+$=3
operators. Indeed, the main objects are instantons and domain walls as the
fully and partially localized objects in the external space, respectively. The
latter comes from an (anti)M5-brane wrapping partly around three internal
directions similar to the fuzzy S^3/Z_k solutions. Except for the first
solutions of adding some anti-M2-branes$\mid$(M2-branes) to the original
M2-branes, the objects backreact on the geometry although small$\mid$(break all
supersymmetries and destabilize the vacua). The dual 3-dimensional field theory
solutions are got by the skew-whiffing 8_s $\rightarrow$ 8_v and 8_s
$\rightarrow$ 8_c for the scalars and pseudoscalars respectively, while the
gauge fields are used mainly for the k=1,2 cases where the R-symmetry and
supersymmetry are enhanced as SU(4) x U(1) $\rightarrow$ SO(8) and N=6
$\rightarrow$ N=8 respectively, and also for pseudoscalars. Further, for the
pseudoscalars we propose a special boundary deformation, with a fermion field,
that is equivalent to a multi-trace deformation already studied for the bulk
m^2=-2 conformally coupled pseudoscalar.
|
[
{
"created": "Wed, 11 Feb 2015 12:31:20 GMT",
"version": "v1"
},
{
"created": "Mon, 30 Mar 2015 22:22:19 GMT",
"version": "v2"
},
{
"created": "Fri, 10 Jul 2015 10:08:55 GMT",
"version": "v3"
}
] |
2015-10-15
|
[
[
"Naghdi",
"M.",
""
]
] |
We consider a few ansatzs for the four and seven forms of 11-dimensional supergravity over AdS_4 x S^7/Z_k while try to keep the geometry unchanged. From the 4-form equations, we arrive at some massless scalars and pseudoscalars in the bulk of Euclidean AdS_4 that match with some boundary $\Delta_+$=3 operators. Indeed, the main objects are instantons and domain walls as the fully and partially localized objects in the external space, respectively. The latter comes from an (anti)M5-brane wrapping partly around three internal directions similar to the fuzzy S^3/Z_k solutions. Except for the first solutions of adding some anti-M2-branes$\mid$(M2-branes) to the original M2-branes, the objects backreact on the geometry although small$\mid$(break all supersymmetries and destabilize the vacua). The dual 3-dimensional field theory solutions are got by the skew-whiffing 8_s $\rightarrow$ 8_v and 8_s $\rightarrow$ 8_c for the scalars and pseudoscalars respectively, while the gauge fields are used mainly for the k=1,2 cases where the R-symmetry and supersymmetry are enhanced as SU(4) x U(1) $\rightarrow$ SO(8) and N=6 $\rightarrow$ N=8 respectively, and also for pseudoscalars. Further, for the pseudoscalars we propose a special boundary deformation, with a fermion field, that is equivalent to a multi-trace deformation already studied for the bulk m^2=-2 conformally coupled pseudoscalar.
|
1807.08062
|
Anderson A. Nogueira
|
A. A. Nogueira, B. M. Pimentel and L. Rabanal
|
Transition amplitude, partition function and the role of physical
degrees of freedom in gauge theories
| null | null |
10.1016/j.nuclphysb.2018.07.024
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
This work explores the quantum dynamics of the interaction between scalar
(matter) and vectorial (intermediate) particles and studies their thermodynamic
equilibrium in the grand-canonical ensemble. The aim of the article is to
clarify the connection between the physical degrees of freedom of a theory in
both the quantization process and the description of the thermodynamic
equilibrium, in which we see an intimate connection between physical degrees of
freedom, Gibbs free energy and the equipartition theorem. We have split the
work into two sections. First, we analyze the quantum interaction in the
context of the generalized scalar Duffin-Kemmer-Petiau quantum electrodynamics
(GSDKP) by using the functional formalism. We build the Hamiltonian structure
following the Dirac methodology, apply the Faddeev-Senjanovic procedure to
obtain the transition amplitude in the generalized Coulomb gauge and, finally,
use the Faddeev-Popov-DeWitt method to write the amplitude in covariant form in
the no-mixing gauge. Subsequently, we exclusively use the Matsubara-Fradkin
(MF) formalism in order to describe fields in thermodynamical equilibrium. The
corresponding equations in thermodynamic equilibrium for the scalar, vectorial
and ghost sectors are explicitly constructed from which the extraction of the
partition function is straightforward. It is in the construction of the
vectorial sector that the emergence and importance of the ghost fields are
revealed: they eliminate the extra non-physical degrees of freedom of the
vectorial sector thus maintaining the physical degrees of freedom.
|
[
{
"created": "Sat, 21 Jul 2018 00:48:45 GMT",
"version": "v1"
}
] |
2018-09-26
|
[
[
"Nogueira",
"A. A.",
""
],
[
"Pimentel",
"B. M.",
""
],
[
"Rabanal",
"L.",
""
]
] |
This work explores the quantum dynamics of the interaction between scalar (matter) and vectorial (intermediate) particles and studies their thermodynamic equilibrium in the grand-canonical ensemble. The aim of the article is to clarify the connection between the physical degrees of freedom of a theory in both the quantization process and the description of the thermodynamic equilibrium, in which we see an intimate connection between physical degrees of freedom, Gibbs free energy and the equipartition theorem. We have split the work into two sections. First, we analyze the quantum interaction in the context of the generalized scalar Duffin-Kemmer-Petiau quantum electrodynamics (GSDKP) by using the functional formalism. We build the Hamiltonian structure following the Dirac methodology, apply the Faddeev-Senjanovic procedure to obtain the transition amplitude in the generalized Coulomb gauge and, finally, use the Faddeev-Popov-DeWitt method to write the amplitude in covariant form in the no-mixing gauge. Subsequently, we exclusively use the Matsubara-Fradkin (MF) formalism in order to describe fields in thermodynamical equilibrium. The corresponding equations in thermodynamic equilibrium for the scalar, vectorial and ghost sectors are explicitly constructed from which the extraction of the partition function is straightforward. It is in the construction of the vectorial sector that the emergence and importance of the ghost fields are revealed: they eliminate the extra non-physical degrees of freedom of the vectorial sector thus maintaining the physical degrees of freedom.
|
1505.04273
|
Tom Banks
|
T. Banks
|
The Temperature/Entropy Connection for Horizons, Massless Particle
Scattering, and the Origin of Locality
| null | null |
10.1142/S0218271815440101
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
I explain, in non-technical terms, the basic ideas of Holographic Space-time
(HST) models of quantum gravity (QG). The key feature is that the degrees of
freedom (DOF) of QG, localized in a finite causal diamond are restrictions of
an algebra of asymptotic currents, describing flows of quantum numbers out to
null infinity in Minkowski space, with zero energy density on the sphere at
infinity. Finite energy density states are constrained states of these DOF and
the resulting relation between asymptotic energy and the number of constraints,
explains the relation between black hole entropy and energy, as well as the
critical energy/impact parameter regime in which particle scattering leads to
black hole formation. The results of a general class of models, implementing
these principles, are described, and applied to understand the firewall
paradox, and to construct a finite model of the early universe, which
implements inflation with only the minimal fine tuning needed to obtain a
universe containing localized excitations more complex than large black holes.
|
[
{
"created": "Sat, 16 May 2015 13:26:45 GMT",
"version": "v1"
}
] |
2015-12-09
|
[
[
"Banks",
"T.",
""
]
] |
I explain, in non-technical terms, the basic ideas of Holographic Space-time (HST) models of quantum gravity (QG). The key feature is that the degrees of freedom (DOF) of QG, localized in a finite causal diamond are restrictions of an algebra of asymptotic currents, describing flows of quantum numbers out to null infinity in Minkowski space, with zero energy density on the sphere at infinity. Finite energy density states are constrained states of these DOF and the resulting relation between asymptotic energy and the number of constraints, explains the relation between black hole entropy and energy, as well as the critical energy/impact parameter regime in which particle scattering leads to black hole formation. The results of a general class of models, implementing these principles, are described, and applied to understand the firewall paradox, and to construct a finite model of the early universe, which implements inflation with only the minimal fine tuning needed to obtain a universe containing localized excitations more complex than large black holes.
|
1003.2877
|
Ruben Manvelyan
|
Ruben Manvelyan, Karapet Mkrtchyan and Werner Ruehl
|
General trilinear interaction for arbitrary even higher spin gauge
fields
|
21 pages, Latex, v.2. minor correction,v.3 final corrections
|
Nucl.Phys.B836:204-221,2010
|
10.1016/j.nuclphysb.2010.04.019
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Using Noether's procedure we present a complete solution for the trilinear
interactions of arbitrary spins $s_{1},s_{2}, s_{3}$ in a flat background, and
discuss the possibility to enlarge this construction to higher order
interactions in the gauge field. Some classification theorems of the cubic
(self)interaction with different numbers of derivatives and depending on
relations between the spins are presented. Finally the expansion of a general
spin $s$ gauge transformation into powers of the field and the related closure
of the gauge algebra in the general case are discussed.
|
[
{
"created": "Mon, 15 Mar 2010 10:13:49 GMT",
"version": "v1"
},
{
"created": "Sat, 14 Jan 2012 07:55:32 GMT",
"version": "v2"
},
{
"created": "Tue, 17 Jan 2012 10:30:30 GMT",
"version": "v3"
}
] |
2012-01-18
|
[
[
"Manvelyan",
"Ruben",
""
],
[
"Mkrtchyan",
"Karapet",
""
],
[
"Ruehl",
"Werner",
""
]
] |
Using Noether's procedure we present a complete solution for the trilinear interactions of arbitrary spins $s_{1},s_{2}, s_{3}$ in a flat background, and discuss the possibility to enlarge this construction to higher order interactions in the gauge field. Some classification theorems of the cubic (self)interaction with different numbers of derivatives and depending on relations between the spins are presented. Finally the expansion of a general spin $s$ gauge transformation into powers of the field and the related closure of the gauge algebra in the general case are discussed.
|
hep-th/9411016
| null |
Simon Hands
|
O(1/N_f) Corrections to the Thirring Model in 2<d<4
|
22 pages in plain TeX, with 7 figs included using psfig.tex (Minor
conceptual changes - algebra unaffected)
|
Phys.Rev. D51 (1995) 5816-5826
|
10.1103/PhysRevD.51.5816
|
SWAT/94/47
|
hep-th hep-lat
| null |
The Thirring model, that is, a relativistic field theory of fermions with a
contact interaction between vector currents, is studied for dimensionalities
2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species.
The model is found to have no ultraviolet divergences at leading order provided
a regularization respecting current conservation is used. Explicit O(1/N_f)
corrections are computed, and the model shown to be renormalizable at this
order in the massless limit; renormalizability appears to hold to all orders
due to a special case of Weinberg's theorem. This implies there is a universal
amplitude for four particle scattering in the asymptotic regime. Comparisons
are made with both the Gross-Neveu model and QED.
|
[
{
"created": "Wed, 2 Nov 1994 14:44:23 GMT",
"version": "v1"
},
{
"created": "Wed, 9 Nov 1994 14:22:00 GMT",
"version": "v2"
},
{
"created": "Thu, 10 Nov 1994 09:47:22 GMT",
"version": "v3"
}
] |
2009-10-28
|
[
[
"Hands",
"Simon",
""
]
] |
The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.
|
1208.4262
|
El Hassan Saidi
|
E.H Saidi, O. Fassi-Fehri, M. Bousmina
|
Topological Aspects of Fermions on Hyperdiamond
|
LaTeX, 56 pages, 6 figures
| null |
10.1063/1.4736835
| null |
hep-th hep-lat
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Motivated by recent results on the index of the Dirac operator
D={\gamma}^{{\mu}}D_{{\mu}} of QCD on lattice and also by results on
topological features of electrons and holes of 2-dimensional graphene, we
compute in this paper the Index of D for fermions living on a family of even
dimensional lattices denoted as L_{2N} and describing the 2N-dimensional
generalization of the graphene honeycomb. The calculation of this topological
Index is done by using the direct method based on solving explicitly the gauged
Dirac equation and also by using specific properties of the lattices L_{2N}
which are shown to be intimately linked with the weight lattices of SU(2N+1).
The Index associated with the two leading N=1 and N=2 elements of this family
describe precisely the chiral anomalies of graphene and QCD_4. Comments on the
method using the spectral flow approach as well as the computation of the
topological charges on 2-cycles of 2N-dimensional compact supercell in L_{2N}
and applications to QCD_4 are also given.
|
[
{
"created": "Tue, 21 Aug 2012 13:36:36 GMT",
"version": "v1"
}
] |
2015-06-11
|
[
[
"Saidi",
"E. H",
""
],
[
"Fassi-Fehri",
"O.",
""
],
[
"Bousmina",
"M.",
""
]
] |
Motivated by recent results on the index of the Dirac operator D={\gamma}^{{\mu}}D_{{\mu}} of QCD on lattice and also by results on topological features of electrons and holes of 2-dimensional graphene, we compute in this paper the Index of D for fermions living on a family of even dimensional lattices denoted as L_{2N} and describing the 2N-dimensional generalization of the graphene honeycomb. The calculation of this topological Index is done by using the direct method based on solving explicitly the gauged Dirac equation and also by using specific properties of the lattices L_{2N} which are shown to be intimately linked with the weight lattices of SU(2N+1). The Index associated with the two leading N=1 and N=2 elements of this family describe precisely the chiral anomalies of graphene and QCD_4. Comments on the method using the spectral flow approach as well as the computation of the topological charges on 2-cycles of 2N-dimensional compact supercell in L_{2N} and applications to QCD_4 are also given.
|
1512.04080
|
Yisong Yang Professor
|
Shouxin Chen and Yisong Yang
|
Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds
|
25 pages
|
Nuclear Physics B 904 (2016) 470--493
|
10.1016/j.nuclphysb.2016.01.021
| null |
hep-th math-ph math.AP math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
An important question concerning the classical solutions of the equations of
motion arising in quantum field theories at the BPS critical coupling is
whether all finite-energy solutions are necessarily BPS. In this paper we
present a study of this basic question in the context of the domain wall
equations whose potential is induced from a superpotential so that the ground
states are the critical points of the superpotential. We prove that the
definiteness of the Hessian of the superpotential suffices to ensure that all
finite-energy domain-wall solutions are BPS. We give several examples to show
that such a BPS property may fail such that non-BPS solutions exist when the
Hessian of the superpotential is indefinite.
|
[
{
"created": "Sun, 13 Dec 2015 16:41:35 GMT",
"version": "v1"
}
] |
2017-09-14
|
[
[
"Chen",
"Shouxin",
""
],
[
"Yang",
"Yisong",
""
]
] |
An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite.
|
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