id stringlengths 9 14 | submitter stringlengths 1 50 ⌀ | authors stringlengths 5 666 | title stringlengths 5 242 | comments stringlengths 1 609 ⌀ | journal-ref stringlengths 9 243 ⌀ | doi stringlengths 12 113 ⌀ | report-no stringlengths 2 204 ⌀ | categories stringlengths 6 112 | license stringclasses 9 values | orig_abstract stringlengths 21 2.11k | versions listlengths 1 26 | update_date stringlengths 10 10 | authors_parsed listlengths 1 38 | abstract stringlengths 18 2.11k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
hep-th/0110094 | Akira Kokado | Akira Kokado, Gaku Konisi and Takesi Saito | NS Open Strings with B Field and Their Interactions with NS Closed
Strings | LaTex, 10 pages, no figures | Prog.Theor.Phys.107:1235-1243,2002 | 10.1143/PTP.107.1235 | null | hep-th | null | We consider interactions of a NS open string with first important states of a
NS closed string, i.e., a closed-string tachyon and a graviton, where both ends
of the NS open string are attached on a D-brane, and a constant background B
field is lying along directions parallel to the D-brane world volume. Contrary
to general expectations, there are no constraints on these vertex operators
coming from the B field. However, we point out that these vertex operators have
singularities at both ends of the NS open string when external momenta take
some values. These kinds of singularities essentially come from the Dirichlet
boundary conditions along directions transverse to the D-brane world volume.
| [
{
"created": "Wed, 10 Oct 2001 06:52:28 GMT",
"version": "v1"
},
{
"created": "Thu, 14 Feb 2002 06:45:42 GMT",
"version": "v2"
}
] | 2014-11-18 | [
[
"Kokado",
"Akira",
""
],
[
"Konisi",
"Gaku",
""
],
[
"Saito",
"Takesi",
""
]
] | We consider interactions of a NS open string with first important states of a NS closed string, i.e., a closed-string tachyon and a graviton, where both ends of the NS open string are attached on a D-brane, and a constant background B field is lying along directions parallel to the D-brane world volume. Contrary to general expectations, there are no constraints on these vertex operators coming from the B field. However, we point out that these vertex operators have singularities at both ends of the NS open string when external momenta take some values. These kinds of singularities essentially come from the Dirichlet boundary conditions along directions transverse to the D-brane world volume. |
0901.4941 | Taizan Watari | Hirotaka Hayashi, Teruhiko Kawano, Radu Tatar and Taizan Watari | Codimension-3 Singularities and Yukawa Couplings in F-theory | 91 pages; minor clarification, typos corrected and a reference added
(v3) | null | 10.1016/j.nuclphysb.2009.07.021 | UT-09-02, LTH 820, IPMU09-0014 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | F-theory is one of the frameworks where all the Yukawa couplings of grand
unified theories are generated and their computation is possible. The Yukawa
couplings of charged matter multiplets are supposed to be generated around
codimension-3 singularity points of a base complex 3-fold, and that has been
confirmed for the simplest type of codimension-3 singularities in recent
studies. However, the geometry of F-theory compactifications is much more
complicated. For a generic F-theory compactification, such issues as flux
configuration around the codimension-3 singularities, field-theory formulation
of the local geometry and behavior of zero-mode wavefunctions have virtually
never been addressed before. We address all these issues in this article, and
further discuss nature of Yukawa couplings generated at such singularities. In
order to calculate the Yukawa couplings of low-energy effective theory,
however, the local descriptions of wavefunctions on complex surfaces and a
global characterization of zero-modes over a complex curve have to be combined
together. We found the relation between them by re-examining how chiral charged
matters are characterized in F-theory compactification. An intrinsic definition
of spectral surfaces in F-theory turns out to be the key concept. As a
biproduct, we found a new way to understand the Heterotic--F theory duality,
which improves the precision of existing duality map associated with
codimension-3 singularities.
| [
{
"created": "Fri, 30 Jan 2009 20:25:45 GMT",
"version": "v1"
},
{
"created": "Mon, 2 Feb 2009 01:05:13 GMT",
"version": "v2"
},
{
"created": "Fri, 13 Feb 2009 01:39:17 GMT",
"version": "v3"
}
] | 2015-05-13 | [
[
"Hayashi",
"Hirotaka",
""
],
[
"Kawano",
"Teruhiko",
""
],
[
"Tatar",
"Radu",
""
],
[
"Watari",
"Taizan",
""
]
] | F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic--F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities. |
2106.14478 | He Ke Jian | Xiao-Xiong Zeng, Guo-Ping Li and Ke-Jian He | The shadows and observational appearance of a noncommutative black hole
surrounded by various profiles of accretions | 25 pages, 12 figures | null | 10.1016/j.nuclphysb.2021.115639 | null | hep-th | http://creativecommons.org/licenses/by/4.0/ | The accretion around the black hole plays a pivotal role in the theoretical
analysis of black hole shadow, and of the black hole observation in particular.
In this paper, we mainly study the shadow and observation characteristics of
noncommutative Schwarzschild black holes wrapped by three accretion models, and
then explore the influence of noncommutative parameters on the observation
appearance and spacetime geometry of black holes. When the black hole is
surrounded by an optically and geometrically thin accretion disk, it shows that
the direct emissions always dominate the total observed intensity, while the
lensing ring superimposed upon the direct emission produces a thin ring, which
improves the observation intensity of the black hole image. However, the photon
rings makes a negligible contributions to the total observed brightness due to
its exponential narrowness, although the photon ring intersects the thin plane
more than three times to pick up larger intensity. More importantly, when the
noncommutative parameters changed, the corresponding regions and observation
intensities of photon ring, lensing ring and direct emission all change
correspondingly. For optical thin spherically symmetric accretion, we consider
the static and infalling matters, respectively. We find that the observation
intensity of the two spherical accretion models increase with the increase of
noncommutative parameters. In addition, due to the Doppler effect of the
infalling movement, the shadow image of infalling accretion is darker than that
of static accretion. In a word, the different accretion models and
noncommutative parameters will lead to different shadow images and optical
appearances of noncommutative Schwarzschild black holes.
| [
{
"created": "Mon, 28 Jun 2021 08:41:21 GMT",
"version": "v1"
},
{
"created": "Wed, 5 Jan 2022 06:31:54 GMT",
"version": "v2"
}
] | 2022-01-26 | [
[
"Zeng",
"Xiao-Xiong",
""
],
[
"Li",
"Guo-Ping",
""
],
[
"He",
"Ke-Jian",
""
]
] | The accretion around the black hole plays a pivotal role in the theoretical analysis of black hole shadow, and of the black hole observation in particular. In this paper, we mainly study the shadow and observation characteristics of noncommutative Schwarzschild black holes wrapped by three accretion models, and then explore the influence of noncommutative parameters on the observation appearance and spacetime geometry of black holes. When the black hole is surrounded by an optically and geometrically thin accretion disk, it shows that the direct emissions always dominate the total observed intensity, while the lensing ring superimposed upon the direct emission produces a thin ring, which improves the observation intensity of the black hole image. However, the photon rings makes a negligible contributions to the total observed brightness due to its exponential narrowness, although the photon ring intersects the thin plane more than three times to pick up larger intensity. More importantly, when the noncommutative parameters changed, the corresponding regions and observation intensities of photon ring, lensing ring and direct emission all change correspondingly. For optical thin spherically symmetric accretion, we consider the static and infalling matters, respectively. We find that the observation intensity of the two spherical accretion models increase with the increase of noncommutative parameters. In addition, due to the Doppler effect of the infalling movement, the shadow image of infalling accretion is darker than that of static accretion. In a word, the different accretion models and noncommutative parameters will lead to different shadow images and optical appearances of noncommutative Schwarzschild black holes. |
1206.4719 | Akikazu Hashimoto | Rajesh Gopakumar, Akikazu Hashimoto, Igor R. Klebanov, Subir Sachdev,
Kareljan Schoutens | Strange Metals in One Spatial Dimension | 40 pages, 4 figures | Physical Review D 86, 066003 (2012) | 10.1103/PhysRevD.86.066003 | PUPT-2419; MAD-TH-12-06 | hep-th cond-mat.str-el | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of
massive Dirac fermions transforming in the adjoint representation of the gauge
group. The only global symmetry of this theory is a U(1) associated with the
conserved Dirac fermion number, and we study the theory at variable, non-zero
densities. The high density limit is characterized by a deconfined Fermi
surface state with Fermi wavevector equal to that of free gauge-charged
fermions. Its low energy fluctuations are described by a coset conformal field
theory with central charge c=(N^2-1)/3 and an emergent N=(2,2) supersymmetry:
the U(1) fermion number symmetry becomes an R-symmetry. We determine the exact
scaling dimensions of the operators associated with Friedel oscillations and
pairing correlations. For N>2, we find that the symmetries allow relevant
perturbations to this state. We discuss aspects of the N->infty limit, and its
possible dual description in AdS3 involving string theory or higher-spin gauge
theory. We also discuss the low density limit of the theory by computing the
low lying bound state spectrum of the large N gauge theory numerically at zero
density, using discretized light cone quantization.
| [
{
"created": "Wed, 20 Jun 2012 20:58:49 GMT",
"version": "v1"
}
] | 2012-09-18 | [
[
"Gopakumar",
"Rajesh",
""
],
[
"Hashimoto",
"Akikazu",
""
],
[
"Klebanov",
"Igor R.",
""
],
[
"Sachdev",
"Subir",
""
],
[
"Schoutens",
"Kareljan",
""
]
] | We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The only global symmetry of this theory is a U(1) associated with the conserved Dirac fermion number, and we study the theory at variable, non-zero densities. The high density limit is characterized by a deconfined Fermi surface state with Fermi wavevector equal to that of free gauge-charged fermions. Its low energy fluctuations are described by a coset conformal field theory with central charge c=(N^2-1)/3 and an emergent N=(2,2) supersymmetry: the U(1) fermion number symmetry becomes an R-symmetry. We determine the exact scaling dimensions of the operators associated with Friedel oscillations and pairing correlations. For N>2, we find that the symmetries allow relevant perturbations to this state. We discuss aspects of the N->infty limit, and its possible dual description in AdS3 involving string theory or higher-spin gauge theory. We also discuss the low density limit of the theory by computing the low lying bound state spectrum of the large N gauge theory numerically at zero density, using discretized light cone quantization. |
hep-th/0404191 | Andre Miemiec | Andre Miemiec, Igor Schnakenburg | Killing Spinor Equations from Nonlinear Realisations | 16 pages, typos corrected | Nucl.Phys. B698 (2004) 517-530 | 10.1016/j.nuclphysb.2004.07.012 | null | hep-th | null | Starting from a nonlinear realisation of eleven dimensional supergravity
based on the group G11, whose generators appear as low level generators of E11,
we present a super extended algebra, which leads to a covariant derivative of
spinors identical to the Killing spinor equation of this theory. A similar
construction leads to the Killing spinor equation of N=1 pure supergravity in
ten dimensions.
| [
{
"created": "Mon, 26 Apr 2004 12:14:05 GMT",
"version": "v1"
},
{
"created": "Tue, 25 May 2004 14:03:20 GMT",
"version": "v2"
}
] | 2007-05-23 | [
[
"Miemiec",
"Andre",
""
],
[
"Schnakenburg",
"Igor",
""
]
] | Starting from a nonlinear realisation of eleven dimensional supergravity based on the group G11, whose generators appear as low level generators of E11, we present a super extended algebra, which leads to a covariant derivative of spinors identical to the Killing spinor equation of this theory. A similar construction leads to the Killing spinor equation of N=1 pure supergravity in ten dimensions. |
2010.11633 | Victor Godet | Antonio M. Garc\'ia-Garc\'ia and Victor Godet | Euclidean wormhole in the SYK model | 27 pages, v2: added discussion on annealed vs quenched, v3: published
version | Phys. Rev. D 103, 046014 (2021) | 10.1103/PhysRevD.103.046014 | null | hep-th cond-mat.str-el | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and
identify a low temperature transition to a gapped phase characterized by a
constant in temperature free energy. This transition is observed without
introducing a coupling between the two sites, and only appears after ensemble
average over the complex couplings. We propose a gravity interpretation of
these results by constructing an explicit solution of Jackiw-Teitelboim (JT)
gravity with matter: a two-dimensional Euclidean wormhole whose geometry is the
double trumpet. This solution is sustained by imaginary sources for a marginal
operator, without the need of a coupling between the two boundaries. As the
temperature is decreased, there is a transition from a disconnected phase with
two black holes to the connected wormhole phase, in qualitative agreement with
the SYK observation. The expectation value of the marginal operator is an order
parameter for this transition. This illustrates in a concrete setup how a
Euclidean wormhole can arise from an average over field theory couplings.
| [
{
"created": "Thu, 22 Oct 2020 12:00:30 GMT",
"version": "v1"
},
{
"created": "Mon, 16 Nov 2020 09:30:45 GMT",
"version": "v2"
},
{
"created": "Mon, 25 Jan 2021 02:47:51 GMT",
"version": "v3"
}
] | 2021-02-24 | [
[
"García-García",
"Antonio M.",
""
],
[
"Godet",
"Victor",
""
]
] | We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and identify a low temperature transition to a gapped phase characterized by a constant in temperature free energy. This transition is observed without introducing a coupling between the two sites, and only appears after ensemble average over the complex couplings. We propose a gravity interpretation of these results by constructing an explicit solution of Jackiw-Teitelboim (JT) gravity with matter: a two-dimensional Euclidean wormhole whose geometry is the double trumpet. This solution is sustained by imaginary sources for a marginal operator, without the need of a coupling between the two boundaries. As the temperature is decreased, there is a transition from a disconnected phase with two black holes to the connected wormhole phase, in qualitative agreement with the SYK observation. The expectation value of the marginal operator is an order parameter for this transition. This illustrates in a concrete setup how a Euclidean wormhole can arise from an average over field theory couplings. |
1402.0740 | Yuki Sato | Naoki Sasakura and Yuki Sato | Exact Free Energies of Statistical Systems on Random Networks | null | SIGMA 10 (2014), 087, 7 pages | 10.3842/SIGMA.2014.087 | WITS-CTP-130, YITP-14-9 | hep-th cond-mat.stat-mech gr-qc | http://creativecommons.org/licenses/by-nc-sa/3.0/ | Statistical systems on random networks can be formulated in terms of
partition functions expressed with integrals by regarding Feynman diagrams as
random networks. We consider the cases of random networks with bounded but
generic degrees of vertices, and show that the free energies can be exactly
evaluated in the thermodynamic limit by the Laplace method, and that the exact
expressions can in principle be obtained by solving polynomial equations for
mean fields. As demonstrations, we apply our method to the ferromagnetic Ising
models on random networks. The free energy of the ferromagnetic Ising model on
random networks with trivalent vertices is shown to exactly reproduce that of
the ferromagnetic Ising model on the Bethe lattice. We also consider the cases
with heterogeneity with mixtures of orders of vertices, and derive the known
formula of the Curie temperature.
| [
{
"created": "Tue, 4 Feb 2014 14:15:27 GMT",
"version": "v1"
},
{
"created": "Wed, 26 Feb 2014 15:59:37 GMT",
"version": "v2"
},
{
"created": "Fri, 15 Aug 2014 05:39:35 GMT",
"version": "v3"
}
] | 2014-08-18 | [
[
"Sasakura",
"Naoki",
""
],
[
"Sato",
"Yuki",
""
]
] | Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of vertices, and show that the free energies can be exactly evaluated in the thermodynamic limit by the Laplace method, and that the exact expressions can in principle be obtained by solving polynomial equations for mean fields. As demonstrations, we apply our method to the ferromagnetic Ising models on random networks. The free energy of the ferromagnetic Ising model on random networks with trivalent vertices is shown to exactly reproduce that of the ferromagnetic Ising model on the Bethe lattice. We also consider the cases with heterogeneity with mixtures of orders of vertices, and derive the known formula of the Curie temperature. |
hep-th/0405209 | Theodora Ioannidou Dr | T.A. Ioannidou, A. Kouiroukidis, N.D. Vlachos | Universality in a Class of Q-Ball Solutions: An Analytic Approach | 9 Pages, 6 Figures | J.Math.Phys. 46 (2005) 042306 | 10.1063/1.1851972 | null | hep-th nlin.SI | null | The properties of Q-balls in the general case of a sixth order potential have
been studied using analytic methods. In particular, for a given potential, the
initial field value that leads to the soliton solution has been derived and the
corresponding energy and charge have been explicitly evaluated. The proposed
scheme is found to work reasonably well for all allowed values of the model
parameters.
| [
{
"created": "Mon, 24 May 2004 14:17:56 GMT",
"version": "v1"
}
] | 2009-11-10 | [
[
"Ioannidou",
"T. A.",
""
],
[
"Kouiroukidis",
"A.",
""
],
[
"Vlachos",
"N. D.",
""
]
] | The properties of Q-balls in the general case of a sixth order potential have been studied using analytic methods. In particular, for a given potential, the initial field value that leads to the soliton solution has been derived and the corresponding energy and charge have been explicitly evaluated. The proposed scheme is found to work reasonably well for all allowed values of the model parameters. |
1912.08135 | Gian Paolo Vacca | A. Bonanno, S. Lippoldt, R. Percacci and G. P. Vacca | On Exact Proper Time Wilsonian RG Flows | 18 pages, 1 figure, revtex, few clarifying comments and references
added | null | 10.1140/epjc/s10052-020-7798-9 | null | hep-th cond-mat.stat-mech | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We discuss the possibility to define exact RG equations for a UV regulated
Wilsonian action based on a proper time (PT) regulator function. We start from
a functional mapping which shows how each particular flow equation (and RG
scheme) is associated to infinitely many scale dependent field redefinitions,
which are related to specific coarse-graining procedures. On specializing to a
sub-family of one parameter PT regulators we briefly analyze few results for
the Ising Universality class in three dimensions, obtained within a second
order truncation in the derivative expansion of the Wilsonian action.
| [
{
"created": "Tue, 17 Dec 2019 16:58:01 GMT",
"version": "v1"
},
{
"created": "Thu, 30 Jan 2020 16:00:02 GMT",
"version": "v2"
}
] | 2020-04-22 | [
[
"Bonanno",
"A.",
""
],
[
"Lippoldt",
"S.",
""
],
[
"Percacci",
"R.",
""
],
[
"Vacca",
"G. P.",
""
]
] | We discuss the possibility to define exact RG equations for a UV regulated Wilsonian action based on a proper time (PT) regulator function. We start from a functional mapping which shows how each particular flow equation (and RG scheme) is associated to infinitely many scale dependent field redefinitions, which are related to specific coarse-graining procedures. On specializing to a sub-family of one parameter PT regulators we briefly analyze few results for the Ising Universality class in three dimensions, obtained within a second order truncation in the derivative expansion of the Wilsonian action. |
2212.07021 | Witold Skiba | Jean-Fran\c{c}ois Fortin, Jingping Li, Alex Sandomirsky, Witold Skiba | Conformal Blocks in Three Dimensions | 40 pages + an appendix and references, 1 figure | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We derive expressions for conformal blocks involving operators with arbitrary
spins in 3-dimensional CFTs. We use previous results on the action of the OPE
in the embedding space to derive the conformal blocks. The blocks are given as
explicit power series in terms of the conformal cross ratios.
| [
{
"created": "Wed, 14 Dec 2022 04:20:23 GMT",
"version": "v1"
}
] | 2022-12-15 | [
[
"Fortin",
"Jean-François",
""
],
[
"Li",
"Jingping",
""
],
[
"Sandomirsky",
"Alex",
""
],
[
"Skiba",
"Witold",
""
]
] | We derive expressions for conformal blocks involving operators with arbitrary spins in 3-dimensional CFTs. We use previous results on the action of the OPE in the embedding space to derive the conformal blocks. The blocks are given as explicit power series in terms of the conformal cross ratios. |
hep-th/0108149 | Chi-Wei Herbert Lee | B. Durhuus and C.-W. H. Lee | A String Bit Hamiltonian Approach to Two-Dimensional Quantum Gravity | 24 pages, no figure; LaTeX2e | Nucl.Phys. B623 (2002) 201-219 | 10.1016/S0550-3213(01)00628-9 | MPS-RR 2001-24 | hep-th gr-qc | null | Motivated by the formalism of string bit models, or quantum matrix models, we
study a class of simple Hamiltonian models of quantum gravity type in two
space-time dimensions. These string bit models are special cases of a more
abstract class of models defined in terms of the sl(2) subalgebra of the
Virasoro algebra. They turn out to be solvable and their scaling limit
coincides in special cases with known transfer matrix models of two-dimensional
quantum gravity.
| [
{
"created": "Tue, 21 Aug 2001 11:11:13 GMT",
"version": "v1"
}
] | 2009-11-07 | [
[
"Durhuus",
"B.",
""
],
[
"Lee",
"C. -W. H.",
""
]
] | Motivated by the formalism of string bit models, or quantum matrix models, we study a class of simple Hamiltonian models of quantum gravity type in two space-time dimensions. These string bit models are special cases of a more abstract class of models defined in terms of the sl(2) subalgebra of the Virasoro algebra. They turn out to be solvable and their scaling limit coincides in special cases with known transfer matrix models of two-dimensional quantum gravity. |
hep-th/0603057 | Shinji Tsujikawa | Edmund J. Copeland, M. Sami, Shinji Tsujikawa | Dynamics of dark energy | 93 pages, 26 figures, Invited Review to be submitted to International
Journal of Modern Physics D; comments are welcome; Additional references
included in response to over 60 comments received. Rewriting of sub-sections
on anthropic principle and gravitational backreaction. New subsections added | Int.J.Mod.Phys.D15:1753-1936,2006 | 10.1142/S021827180600942X | null | hep-th astro-ph gr-qc hep-ph | null | In this paper we review in detail a number of approaches that have been
adopted to try and explain the remarkable observation of our accelerating
Universe. In particular we discuss the arguments for and recent progress made
towards understanding the nature of dark energy. We review the observational
evidence for the current accelerated expansion of the universe and present a
number of dark energy models in addition to the conventional cosmological
constant, paying particular attention to scalar field models such as
quintessence, K-essence, tachyon, phantom and dilatonic models. The importance
of cosmological scaling solutions is emphasized when studying the dynamical
system of scalar fields including coupled dark energy. We study the evolution
of cosmological perturbations allowing us to confront them with the observation
of the Cosmic Microwave Background and Large Scale Structure and demonstrate
how it is possible in principle to reconstruct the equation of state of dark
energy by also using Supernovae Ia observational data. We also discuss in
detail the nature of tracking solutions in cosmology, particle physics and
braneworld models of dark energy, the nature of possible future singularities,
the effect of higher order curvature terms to avoid a Big Rip singularity, and
approaches to modifying gravity which leads to a late-time accelerated
expansion without recourse to a new form of dark energy.
| [
{
"created": "Wed, 8 Mar 2006 01:25:15 GMT",
"version": "v1"
},
{
"created": "Fri, 10 Mar 2006 13:44:15 GMT",
"version": "v2"
},
{
"created": "Fri, 16 Jun 2006 10:46:50 GMT",
"version": "v3"
}
] | 2008-11-26 | [
[
"Copeland",
"Edmund J.",
""
],
[
"Sami",
"M.",
""
],
[
"Tsujikawa",
"Shinji",
""
]
] | In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy. |
1408.3885 | Mayumi Saitou | Mayumi Saitou, Kazuharu Bamba and Akio Sugamoto | Hydrodynamics on non-commutative space --A step toward hydrodynamics of
granular materials-- | 19 pages, no figure, version accepted for publication in Progress of
Theoretical and Experimental Physics | Progress of Theoretical and Experimental Physics (2014) 103B03 | 10.1093/ptep/ptu138 | OCHA-PP-327 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Hydrodynamics on non-commutative space is studied based on a formulation of
hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing
these brackets by Moyal brackets with a parameter $\theta$, a new hydrodynamics
on non-commutative space is derived. It may be a step toward to find the
hydrodynamics of granular materials whose minimum volume is given by $\theta$.
To clarify this minimum volume, path integral quantization and uncertainty
relation of Nambu dynamics are examined.
| [
{
"created": "Mon, 18 Aug 2014 02:00:19 GMT",
"version": "v1"
},
{
"created": "Tue, 19 Aug 2014 08:04:59 GMT",
"version": "v2"
},
{
"created": "Tue, 16 Sep 2014 06:18:13 GMT",
"version": "v3"
}
] | 2014-10-22 | [
[
"Saitou",
"Mayumi",
""
],
[
"Bamba",
"Kazuharu",
""
],
[
"Sugamoto",
"Akio",
""
]
] | Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter $\theta$, a new hydrodynamics on non-commutative space is derived. It may be a step toward to find the hydrodynamics of granular materials whose minimum volume is given by $\theta$. To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined. |
2407.18019 | Thomas Helpin | Thomas Helpin | Irreducible decompositions of tensors via the Brauer algebra and
applications to metric-affine gravity | 186 pages, PhD manuscript | null | null | null | hep-th gr-qc math-ph math.MP math.RT | http://creativecommons.org/licenses/by/4.0/ | In the first part of this thesis, we make use of representation theory of
groups and algebras to perform an irreducible decomposition of tensors in the
context of metric-affine gravity. In particular, we consider the action of the
orthogonal group O(1, d$-1$) on the Riemann tensor associated with an affine
connection defined on a d-dimensional pseudo-Riemannian manifold. This
connection, with torsion and non-metricity, is the characteristic ingredient of
metric-affine theories of gravity.
In the second part of this thesis, we construct the projection operators used
for the aforementioned decomposition. They are realized in terms of the
symmetric group algebra $\mathbb{C}\mathfrak{S}_n$ and of the Brauer algebra
B$_n$(d) which are related respectively to the action of GL(d,$\mathbb{C}$)
(and its real form GL(d,$\mathbb{R}$)) and to the action of O(d,$\mathbb{C}$)
(and its real form O(1 , d$-1$)) on tensors via the Schur-Weyl duality. First
of all, we give an alternative approach to the known formulas for the central
idempotents of $\mathbb{C}\mathfrak{S}_n$. These elements provide a unique
reducible decomposition, known as the isotypic decomposition. For our purposes,
this decomposition is remarkably handy to arrive at the sought after
irreducible decomposition with respect to GL(d,$\mathbb{R}$). Then, we
construct the elements in B$_n$(d) which realize the isotypic decomposition of
a tensor under the action of O(d,$\mathbb{C}$). This decomposition is
irreducible under O(d,$\mathbb{C}$) when applied to an irreducible
GL(d,$\mathbb{C}$) tensor of order $5$ or less. As a by product of the
construction, we give a solution to the problem of decomposing an arbitrary
tensor into its traceless part, doubly traceless part and so on. These results
led to the development of several Mathematica packages linked to the
\textit{xAct} bundle for tensor calculus in field theory.
| [
{
"created": "Thu, 25 Jul 2024 13:13:10 GMT",
"version": "v1"
}
] | 2024-07-26 | [
[
"Helpin",
"Thomas",
""
]
] | In the first part of this thesis, we make use of representation theory of groups and algebras to perform an irreducible decomposition of tensors in the context of metric-affine gravity. In particular, we consider the action of the orthogonal group O(1, d$-1$) on the Riemann tensor associated with an affine connection defined on a d-dimensional pseudo-Riemannian manifold. This connection, with torsion and non-metricity, is the characteristic ingredient of metric-affine theories of gravity. In the second part of this thesis, we construct the projection operators used for the aforementioned decomposition. They are realized in terms of the symmetric group algebra $\mathbb{C}\mathfrak{S}_n$ and of the Brauer algebra B$_n$(d) which are related respectively to the action of GL(d,$\mathbb{C}$) (and its real form GL(d,$\mathbb{R}$)) and to the action of O(d,$\mathbb{C}$) (and its real form O(1 , d$-1$)) on tensors via the Schur-Weyl duality. First of all, we give an alternative approach to the known formulas for the central idempotents of $\mathbb{C}\mathfrak{S}_n$. These elements provide a unique reducible decomposition, known as the isotypic decomposition. For our purposes, this decomposition is remarkably handy to arrive at the sought after irreducible decomposition with respect to GL(d,$\mathbb{R}$). Then, we construct the elements in B$_n$(d) which realize the isotypic decomposition of a tensor under the action of O(d,$\mathbb{C}$). This decomposition is irreducible under O(d,$\mathbb{C}$) when applied to an irreducible GL(d,$\mathbb{C}$) tensor of order $5$ or less. As a by product of the construction, we give a solution to the problem of decomposing an arbitrary tensor into its traceless part, doubly traceless part and so on. These results led to the development of several Mathematica packages linked to the \textit{xAct} bundle for tensor calculus in field theory. |
2010.06895 | Alessandro Georgoudis | Dominik Bendle, Janko Boehm, Wolfram Decker, Alessandro Georgoudis,
Franz-Josef Pfreundt, Mirko Rahn and Yang Zhang | Module Intersection for the Integration-by-Parts Reduction of Multi-Loop
Feynman Integrals | 19 pages, 5 figures. To appear in the proceedings of
"MathemAmplitudes 2019: Intersection Theory & Feynman Integrals", held in
Padova 18-20 December 2019 | null | null | null | hep-th hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this manuscript, which is to appear in the proceedings of the conference
"MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module
intersection method for the the integration-by-parts (IBP) reduction of
multi-loop Feynman integrals. The module intersection method, based on
computational algebraic geometry, is a highly efficient way of getting IBP
relations without double propagator or with a bound on the highest propagator
degree. In this manner, trimmed IBP systems which are much shorter than the
traditional ones can be obtained. We apply the modern, Petri net based,
workflow management system GPI-Space in combination with the computer algebra
system Singular to solve the trimmed IBP system via interpolation and efficient
parallelization. We show, in particular, how to use the new plugin feature of
GPI-Space to manage a global state of the computation and to efficiently handle
mutable data. Moreover, a Mathematica interface to generate IBPs with
restricted propagator degree, which is based on module intersection, is
presented in this review.
| [
{
"created": "Wed, 14 Oct 2020 09:08:09 GMT",
"version": "v1"
}
] | 2020-10-15 | [
[
"Bendle",
"Dominik",
""
],
[
"Boehm",
"Janko",
""
],
[
"Decker",
"Wolfram",
""
],
[
"Georgoudis",
"Alessandro",
""
],
[
"Pfreundt",
"Franz-Josef",
""
],
[
"Rahn",
"Mirko",
""
],
[
"Zhang",
"Yang",
""
]
] | In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for the the integration-by-parts (IBP) reduction of multi-loop Feynman integrals. The module intersection method, based on computational algebraic geometry, is a highly efficient way of getting IBP relations without double propagator or with a bound on the highest propagator degree. In this manner, trimmed IBP systems which are much shorter than the traditional ones can be obtained. We apply the modern, Petri net based, workflow management system GPI-Space in combination with the computer algebra system Singular to solve the trimmed IBP system via interpolation and efficient parallelization. We show, in particular, how to use the new plugin feature of GPI-Space to manage a global state of the computation and to efficiently handle mutable data. Moreover, a Mathematica interface to generate IBPs with restricted propagator degree, which is based on module intersection, is presented in this review. |
hep-th/9801123 | Tianjun Li | Tianjun Li | Compactification and Supersymmetry Breaking in M-theory | 16 pages, latex, no figures | Phys.Rev.D57:7539-7545,1998 | 10.1103/PhysRevD.57.7539 | null | hep-th hep-ph | null | Keeping N=1 supersymmetry in 4-dimension and in the leading order, we disuss
the various orbifold compactifications of M-theory suggested by Horava and
Witten on $T^6/Z_3$, $T^6/Z_6$, $T^6/Z_{12}$, and the compactification by
keeping singlets under $SU(2)\times U(1)$ symmetry, then the compactification
on $S^1/Z_2$. We also discuss the next to leading order K\"ahler potential,
superpotential, and gauge kinetic function in the $Z_{12}$ case. In addition,
we calculate the SUSY breaking soft terms and find out that the universality of
the scalar masses will be violated, but the violation might be very small.
| [
{
"created": "Sun, 18 Jan 1998 19:25:01 GMT",
"version": "v1"
}
] | 2010-11-19 | [
[
"Li",
"Tianjun",
""
]
] | Keeping N=1 supersymmetry in 4-dimension and in the leading order, we disuss the various orbifold compactifications of M-theory suggested by Horava and Witten on $T^6/Z_3$, $T^6/Z_6$, $T^6/Z_{12}$, and the compactification by keeping singlets under $SU(2)\times U(1)$ symmetry, then the compactification on $S^1/Z_2$. We also discuss the next to leading order K\"ahler potential, superpotential, and gauge kinetic function in the $Z_{12}$ case. In addition, we calculate the SUSY breaking soft terms and find out that the universality of the scalar masses will be violated, but the violation might be very small. |
1412.1819 | Lihui Liu | Lihui Liu | Holographic renormalization in no-boundary quantum cosmology | 68 pages 32 figures; In v2: typos eliminated; a misjudge of mass
range in 3d corrected, related contents revised in Sec.2.3, Sec.7 and
appendix B; the 4d example in Sec.6.2 is replaced by a 5d one, due to
possible author right clash with another paper in preparation; references
added or updated | null | null | null | hep-th gr-qc quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Recent results of Hartle-Hawking wave functions on asymptotic dS boundaries
show non-normalizability, while the bulk origin is not clear. This paper
attempts to addresse this problem by studying (Kerr-)dS_3 cosmology in Einstein
gravity deformed by a minimally coupled scalar field. Various saddle-point
contributions exp[i(saddle-point action)] to the Hartle-Hawking wave functions
are computed with mini-superspace formalism. The saddle-point actions are first
obtained in the spacetime bulks by direct computation, then on the asymptotic
dS boundary by holographic renormalization. It is found that the imaginary part
of the saddle-point actions, as functions of scalar field deformation, are
generally bounded in the bulk, but can diverge to -infty on the boundary. This
can probably be a source of the scalar field-related non-normalizability of the
boundary Hartle-Hawking wave functions. For Kerr-dS_3 cosmology, some
saddle-point actions have imaginary parts diverging to -infty both in the bulk
and on the boundary, when the boundary T^2 is stretched to infinitely long.
This can be an origin of non-normalizability of the boundary Hartle-Hawking
wave functions related to temperature divergence. Finally the holographic
renormalization is extended to scalar-deformed dS_{d+1} (d>= 3) cosmologies for
the imaginary part of the saddle-point actions. The result is tested on a 5d
example, and saddle points leading to divergent contribution to the boundary
Hartle-Hawking wave function are shown to exist.
| [
{
"created": "Thu, 4 Dec 2014 20:59:30 GMT",
"version": "v1"
},
{
"created": "Mon, 22 Dec 2014 17:36:31 GMT",
"version": "v2"
}
] | 2014-12-23 | [
[
"Liu",
"Lihui",
""
]
] | Recent results of Hartle-Hawking wave functions on asymptotic dS boundaries show non-normalizability, while the bulk origin is not clear. This paper attempts to addresse this problem by studying (Kerr-)dS_3 cosmology in Einstein gravity deformed by a minimally coupled scalar field. Various saddle-point contributions exp[i(saddle-point action)] to the Hartle-Hawking wave functions are computed with mini-superspace formalism. The saddle-point actions are first obtained in the spacetime bulks by direct computation, then on the asymptotic dS boundary by holographic renormalization. It is found that the imaginary part of the saddle-point actions, as functions of scalar field deformation, are generally bounded in the bulk, but can diverge to -infty on the boundary. This can probably be a source of the scalar field-related non-normalizability of the boundary Hartle-Hawking wave functions. For Kerr-dS_3 cosmology, some saddle-point actions have imaginary parts diverging to -infty both in the bulk and on the boundary, when the boundary T^2 is stretched to infinitely long. This can be an origin of non-normalizability of the boundary Hartle-Hawking wave functions related to temperature divergence. Finally the holographic renormalization is extended to scalar-deformed dS_{d+1} (d>= 3) cosmologies for the imaginary part of the saddle-point actions. The result is tested on a 5d example, and saddle points leading to divergent contribution to the boundary Hartle-Hawking wave function are shown to exist. |
0712.0350 | Jerzy Lukierski | Marcin Daszkiewicz, Jerzy Lukierski and Mariusz Woronowicz | Quantization of kappa-deformed free fields and kappa-deformed
oscillators | 9 pages. Talk presented at Supersymmetry and Quantum Supersymmetry
2007 (SQS'07) Conference (Dubna, 30.07-4.08.2007) and IV-th Central European
Seminar "Commutative and Noncommutative Quantum Fields" (Vienna,
30.11-2.12.2007). To be published in the proceedings of SQS'07 (2008) | null | null | null | hep-th | null | We describe the deformed E.T. quantization rules for kappa-deformed free
quantum fields, and relate these rules with the kappa-deformed algebra of field
oscillators.
| [
{
"created": "Mon, 3 Dec 2007 17:15:55 GMT",
"version": "v1"
}
] | 2007-12-04 | [
[
"Daszkiewicz",
"Marcin",
""
],
[
"Lukierski",
"Jerzy",
""
],
[
"Woronowicz",
"Mariusz",
""
]
] | We describe the deformed E.T. quantization rules for kappa-deformed free quantum fields, and relate these rules with the kappa-deformed algebra of field oscillators. |
0807.0213 | Dionisio Bazeia | D. Bazeia, L. Losano, R. Menezes | First-order framework and generalized global defect solutions | 8 pages, 6 figures; version to appear in PLB | Phys.Lett.B668:246-252,2008 | 10.1016/j.physletb.2008.08.046 | null | hep-th astro-ph hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This work deals with defect structures in models described by scalar fields.
The investigations focus on generalized models, with the kinetic term modified
to allow for a diversity of possibilities. We develop a new framework, in which
we search for first-order differential equations which solve the equations of
motion. The main issue concerns the introduction of a new function, which works
like the superpotential usually considered in the standard situation. We
investigate the problem in the general case, with an arbitrary number of
fields, and we present several explicit examples in the case of a single real
scalar field.
| [
{
"created": "Tue, 1 Jul 2008 18:26:49 GMT",
"version": "v1"
},
{
"created": "Thu, 21 Aug 2008 20:04:28 GMT",
"version": "v2"
}
] | 2010-05-12 | [
[
"Bazeia",
"D.",
""
],
[
"Losano",
"L.",
""
],
[
"Menezes",
"R.",
""
]
] | This work deals with defect structures in models described by scalar fields. The investigations focus on generalized models, with the kinetic term modified to allow for a diversity of possibilities. We develop a new framework, in which we search for first-order differential equations which solve the equations of motion. The main issue concerns the introduction of a new function, which works like the superpotential usually considered in the standard situation. We investigate the problem in the general case, with an arbitrary number of fields, and we present several explicit examples in the case of a single real scalar field. |
hep-th/9906162 | J. P. Gauntlett | Jerome P. Gauntlett | Membranes on Fivebranes | Latex, 14 pages. Minor corrections. Version to be published in Adv.
Theor. Math. Phys | Adv.Theor.Math.Phys. 3 (1999) 775-790 | null | QMW-99-08 | hep-th | null | By analysing supersymmetry transformations we derive new BPS equations for
the D=11 fivebrane propagating in flat space that involve the world-volume
three-form. The equations generalise those of 2,3,4 and 5 dimensional special
Lagrangian submanifolds and are relevant for describing membranes ending on
these submanifolds.
| [
{
"created": "Mon, 21 Jun 1999 15:24:12 GMT",
"version": "v1"
},
{
"created": "Fri, 22 Oct 1999 08:33:35 GMT",
"version": "v2"
}
] | 2007-05-23 | [
[
"Gauntlett",
"Jerome P.",
""
]
] | By analysing supersymmetry transformations we derive new BPS equations for the D=11 fivebrane propagating in flat space that involve the world-volume three-form. The equations generalise those of 2,3,4 and 5 dimensional special Lagrangian submanifolds and are relevant for describing membranes ending on these submanifolds. |
2203.16112 | Qinglin Yang | Qinglin Yang | Schubert Problems, Positivity and Symbol Letters | 19 pages, 4 figures | null | 10.1007/JHEP08(2022)168 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We propose a geometrical approach to generate symbol letters of
amplitudes/integrals in planar $\mathcal{N}=4$ Super Yang-Mills theory, known
as {\it Schubert problems}. Beginning with one-loop integrals, we find that
intersections of lines in momentum twistor space are always ordered on a given
line, once the external kinematics $\mathbf{Z}$ is in the positive region
$G_+(4,n)$. Remarkably, cross-ratios of these ordered intersections on a line,
which are guaranteed to be positive now, nicely coincide with symbol letters of
corresponding Feynman integrals, whose positivity is then concluded directly
from such geometrical configurations. In particular, we reproduce from this
approach the $18$ multiplicative independent algebraic letters for $n=8$
amplitudes up to three loops. Finally, we generalize the discussion to two-loop
Schubert problems and, again from ordered points on a line, generate a new kind
of algebraic letters which mix two distinct square roots together. They have
been found recently in the alphabet of two-loop double-box integral with
$n\geq9$, and they are expected to appear in amplitudes at $k+\ell\geq4$.
| [
{
"created": "Wed, 30 Mar 2022 07:43:12 GMT",
"version": "v1"
}
] | 2022-09-07 | [
[
"Yang",
"Qinglin",
""
]
] | We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar $\mathcal{N}=4$ Super Yang-Mills theory, known as {\it Schubert problems}. Beginning with one-loop integrals, we find that intersections of lines in momentum twistor space are always ordered on a given line, once the external kinematics $\mathbf{Z}$ is in the positive region $G_+(4,n)$. Remarkably, cross-ratios of these ordered intersections on a line, which are guaranteed to be positive now, nicely coincide with symbol letters of corresponding Feynman integrals, whose positivity is then concluded directly from such geometrical configurations. In particular, we reproduce from this approach the $18$ multiplicative independent algebraic letters for $n=8$ amplitudes up to three loops. Finally, we generalize the discussion to two-loop Schubert problems and, again from ordered points on a line, generate a new kind of algebraic letters which mix two distinct square roots together. They have been found recently in the alphabet of two-loop double-box integral with $n\geq9$, and they are expected to appear in amplitudes at $k+\ell\geq4$. |
1904.08419 | Eugenio R. Bezerra de Mello | W. Oliveira dos Santos, E. R. Bezerra de Mello and H. F. Mota | Vacuum polarization in high-dimensional AdS spacetime in the presence of
a cosmic string and compactified extra dimension | 21 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1809.00702 Version accepted for publication in the EPJP | Eur. Phys. J. Plus (2020) 135:27 | 10.1140/epjp/s13360-019-00057-4 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we analyze the vacuum expectation values (VEVs) of the field
squared and the energy-momentum tensor associated with a charged and massive
scalar quantum field in a generalized $(D+1)$-dimensional anti-de Sitter space
in the presence of a cosmic string, admitting a magnetic flux running along the
string's core. In addition we admit that an extra coordinate is compactified to
a circle and presents a magnetic flux running along its center. This
compactification is implemented by imposing a quasiperiodic condition on the
field with an arbitrary phase. The calculation of the VEVs of the field squared
and the energy-moment tensor, are developed by using positive-energy Wightman
function. The latter is construct by the mode sum over the complete set of
normalized bosonic wavefunctions. Due to the compactification, the Wightman
function is presented as the sum of two distinct contributions. The first one
corresponding to the idealized cosmic string, and the second is induced by the
compactification. The latter goes to zero for an infinite length of the
compactification. As a consequence of the general structure of the Wightman
function, both VEVs present also this decomposition. Moreover, due to the
Aharanov-Bohm type of interaction between the field with the magnetic fluxes,
the VEVs depend on the fractional part of the ration between the total flux and
the quantum one.
| [
{
"created": "Wed, 17 Apr 2019 13:17:39 GMT",
"version": "v1"
},
{
"created": "Tue, 1 Oct 2019 13:03:35 GMT",
"version": "v2"
}
] | 2020-01-15 | [
[
"Santos",
"W. Oliveira dos",
""
],
[
"de Mello",
"E. R. Bezerra",
""
],
[
"Mota",
"H. F.",
""
]
] | In this paper, we analyze the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a charged and massive scalar quantum field in a generalized $(D+1)$-dimensional anti-de Sitter space in the presence of a cosmic string, admitting a magnetic flux running along the string's core. In addition we admit that an extra coordinate is compactified to a circle and presents a magnetic flux running along its center. This compactification is implemented by imposing a quasiperiodic condition on the field with an arbitrary phase. The calculation of the VEVs of the field squared and the energy-moment tensor, are developed by using positive-energy Wightman function. The latter is construct by the mode sum over the complete set of normalized bosonic wavefunctions. Due to the compactification, the Wightman function is presented as the sum of two distinct contributions. The first one corresponding to the idealized cosmic string, and the second is induced by the compactification. The latter goes to zero for an infinite length of the compactification. As a consequence of the general structure of the Wightman function, both VEVs present also this decomposition. Moreover, due to the Aharanov-Bohm type of interaction between the field with the magnetic fluxes, the VEVs depend on the fractional part of the ration between the total flux and the quantum one. |
hep-th/0303080 | Stefan Waldmann | Stefan Waldmann | Deformation Quantization: Observable Algebras, States and Representation
Theory | LaTeX2e, 32 pages. Lecture notes for the Kopaonik summer school 2002 | null | null | FR-THEP 2003/04 | hep-th math.QA | null | In these lecture notes I give an introduction to deformation quantization.
The quantization problem is discussed in some detail thereby motivating the
notion of star products. Starting from a deformed observable algebra, i.e. the
star product algebra, physical applications require to study representations of
this algebra. I review the recent development of a representation theory
including techniques like Rieffel induction and Morita equivalence.
Applications beyond quantization theory are found in noncommutative field
theories.
| [
{
"created": "Mon, 10 Mar 2003 15:05:53 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Waldmann",
"Stefan",
""
]
] | In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star product algebra, physical applications require to study representations of this algebra. I review the recent development of a representation theory including techniques like Rieffel induction and Morita equivalence. Applications beyond quantization theory are found in noncommutative field theories. |
hep-th/0008027 | Parameswaran Nair | V.P. Nair | Quantum Mechanics on a Noncommutative Brane in M(atrix) Theory | Minor changes, report number changed, references added, 9 pages,
LaTeX | Phys.Lett. B505 (2001) 249-254 | 10.1016/S0370-2693(01)00338-0 | CCNY-HEP 00/3, RU-00-8-B | hep-th | null | We consider the quantum mechanics of a particle on a noncommutative
two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator
can be constructed in terms of an $SU(2)\times SU(2)$-extension and the
Heisenberg algebra recovered in the smooth manifold limit. Similar
considerations apply to the more general SU(n) case.
| [
{
"created": "Wed, 2 Aug 2000 19:11:06 GMT",
"version": "v1"
},
{
"created": "Tue, 14 Nov 2000 03:03:02 GMT",
"version": "v2"
}
] | 2016-09-06 | [
[
"Nair",
"V. P.",
""
]
] | We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra recovered in the smooth manifold limit. Similar considerations apply to the more general SU(n) case. |
hep-th/9610197 | Gernot Muenster | Gernot M\"unster (University of M\"unster), Harald Grie{\ss}hammer and
Dirk Lehmann (University of Erlangen) | Field Theory, Critical Phenomena and Interfaces | 21 pages, LaTeX, 4 Postscript figures, uses epsf.sty, Talk by G.M.
presented to the Graduiertenkolleg Erlangen-Regensburg | null | null | MS-TPI-96-17, FAU-TP3-96/16 | hep-th cond-mat | null | These lecture notes want to illustrate the close connection between
statistical mechanics and field theory not only on the formal level, i.e. that
many concepts of one area can easily be taken over to the other one, but also
on the level of actual calculations. To this purpose, the last section will
demonstrate that a special statistical system, the binary fluid system, can be
described by field theory in its critical behaviour.
| [
{
"created": "Fri, 25 Oct 1996 09:35:38 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Münster",
"Gernot",
"",
"University of Münster"
],
[
"Grießhammer",
"Harald",
"",
"University of Erlangen"
],
[
"Lehmann",
"Dirk",
"",
"University of Erlangen"
]
] | These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of actual calculations. To this purpose, the last section will demonstrate that a special statistical system, the binary fluid system, can be described by field theory in its critical behaviour. |
2407.20747 | H. W. Braden | H. W. Braden and Linden Disney-Hogg | Dihedrally Symmetric Monopoles and Affine Toda Equations | 22 pages; 2 figures | null | null | null | hep-th math-ph math.MP nlin.SI | http://creativecommons.org/licenses/by/4.0/ | We show that any $SU(2)$ BPS monopole of charge $k$ with rotational spatial
dihedral symmetry is gauge equivalent to the Nahm data obtained from affine
Toda equations of $C_l^{(1)}$ type when $k=2l$ or $A_{2(l-1)}^{(2)}$ type when
$k=2l-1$.
| [
{
"created": "Tue, 30 Jul 2024 11:32:54 GMT",
"version": "v1"
}
] | 2024-07-31 | [
[
"Braden",
"H. W.",
""
],
[
"Disney-Hogg",
"Linden",
""
]
] | We show that any $SU(2)$ BPS monopole of charge $k$ with rotational spatial dihedral symmetry is gauge equivalent to the Nahm data obtained from affine Toda equations of $C_l^{(1)}$ type when $k=2l$ or $A_{2(l-1)}^{(2)}$ type when $k=2l-1$. |
1807.11304 | Wei Li | Matthias R. Gaberdiel, Wei Li and Cheng Peng | Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian | 61 pages, 14 figures, 2 tables | null | 10.1007/JHEP11(2018)192 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The universal enveloping algebra of ${\cal W}_{1+\infty}$ is isomorphic to
the affine Yangian of $\mathfrak{gl}_1$. We study the ${\cal N}=2$
supersymmetric version of this correspondence, and identify the full set of
defining relations of the supersymmetric affine Yangian. These relations can be
deduced by demanding that the algebra has a representation on
twin-plane-partitions, which we construct by gluing pairs of plane partitions.
We define the action of the algebra on these twin-plane-partitions explicitly.
| [
{
"created": "Mon, 30 Jul 2018 12:07:18 GMT",
"version": "v1"
}
] | 2018-12-26 | [
[
"Gaberdiel",
"Matthias R.",
""
],
[
"Li",
"Wei",
""
],
[
"Peng",
"Cheng",
""
]
] | The universal enveloping algebra of ${\cal W}_{1+\infty}$ is isomorphic to the affine Yangian of $\mathfrak{gl}_1$. We study the ${\cal N}=2$ supersymmetric version of this correspondence, and identify the full set of defining relations of the supersymmetric affine Yangian. These relations can be deduced by demanding that the algebra has a representation on twin-plane-partitions, which we construct by gluing pairs of plane partitions. We define the action of the algebra on these twin-plane-partitions explicitly. |
hep-th/0401060 | Deog Ki Hong | Deog Ki Hong (Pusan Nat'l Univ.) and Stephen D. H. Hsu (U. of Oregon) | Brane World Confronts Holography | 5 pages, 5 figures, revtex 4, Talk by DKH at 2nd International
Conference on Flavor Physics (ICFP 2003), Seoul, Korea, 6-11 Oct 2003 | J.Korean Phys.Soc. 45 (2004) S273-S277 | null | PNUTP-04/A01 | hep-th | null | Holography principle imposes a stringent constraint on the scale of quantum
gravity $M_*$ in brane-world scenarios, where all matter is confined on the
brane. The thermodynamic entropy of astrophysical black holes and sub-horizon
volumes during big bang nucleosynthesis exceed the relevant bounds unless $M_*
> 10^{(4-6)}$ TeV, so a hierarchy relative to the weak scale is unavoidable. We
discuss the implications for extra dimensions as well as holography.
| [
{
"created": "Sat, 10 Jan 2004 05:03:44 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Hong",
"Deog Ki",
"",
"Pusan Nat'l Univ."
],
[
"Hsu",
"Stephen D. H.",
"",
"U. of Oregon"
]
] | Holography principle imposes a stringent constraint on the scale of quantum gravity $M_*$ in brane-world scenarios, where all matter is confined on the brane. The thermodynamic entropy of astrophysical black holes and sub-horizon volumes during big bang nucleosynthesis exceed the relevant bounds unless $M_* > 10^{(4-6)}$ TeV, so a hierarchy relative to the weak scale is unavoidable. We discuss the implications for extra dimensions as well as holography. |
1507.05650 | Zitao Wang | Ning Bao, ChunJun Cao, Michael Walter, Zitao Wang | Holographic entropy inequalities and gapped phases of matter | 20 pages, 4 figures. v2: section 4 rewritten, where all linear
entropy (in)equalities satisfied by area-law systems are derived and an error
in their relations to graph theory is corrected | JHEP 1509:203,2015 | 10.1007/JHEP09(2015)203 | CALT-TH-2015-041 | hep-th cond-mat.str-el quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We extend our studies of holographic entropy inequalities to gapped phases of
matter. For any number of regions, we determine the linear entropy inequalities
satisfied by systems in which the entanglement entropy satisfies an exact area
law. In particular, we find that all holographic entropy inequalities are valid
in such systems. In gapped systems with topological order, the "cyclic
inequalities" derived recently for the holographic entanglement entropy
generalize the Kitaev-Preskill formula for the topological entanglement
entropy. Finally, we propose a candidate linear inequality for general 4-party
quantum states.
| [
{
"created": "Mon, 20 Jul 2015 20:50:04 GMT",
"version": "v1"
},
{
"created": "Sun, 26 Jul 2015 19:57:29 GMT",
"version": "v2"
}
] | 2015-10-02 | [
[
"Bao",
"Ning",
""
],
[
"Cao",
"ChunJun",
""
],
[
"Walter",
"Michael",
""
],
[
"Wang",
"Zitao",
""
]
] | We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the "cyclic inequalities" derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states. |
hep-th/9701143 | Roberto Iengo | Faheem Hussain, Roberto Iengo and Carmen N\'u\~nez | Axion production from gravitons off interacting 0-branes | 39 pages, Latex, 3 figures | Nucl.Phys.B497:205-235,1997 | 10.1016/S0550-3213(97)00238-1 | IC/97/1, SISSAREF-3/97/EP | hep-th | null | We study axion-graviton scattering from a system of two D$0$-branes in a Type
II superstring theory, a process which does not occur on a single brane. The
two D$0$-branes interact via the exchange of closed string states which form a
cylinder joining them. By compactifying on the $Z_3$ orbifold we find a non
vanishing amplitude coming from the odd spin structure sector, thus from the
exchanged RR states. We compute, in particular, the leading term of the
amplitude at large distance from the branes, which corresponds to taking a
field theory limit. This seems to suggest that the process takes place through
the coupling of an axion to the RR states exchanged between the 0-branes.
| [
{
"created": "Mon, 27 Jan 1997 13:30:51 GMT",
"version": "v1"
}
] | 2009-03-27 | [
[
"Hussain",
"Faheem",
""
],
[
"Iengo",
"Roberto",
""
],
[
"Núñez",
"Carmen",
""
]
] | We study axion-graviton scattering from a system of two D$0$-branes in a Type II superstring theory, a process which does not occur on a single brane. The two D$0$-branes interact via the exchange of closed string states which form a cylinder joining them. By compactifying on the $Z_3$ orbifold we find a non vanishing amplitude coming from the odd spin structure sector, thus from the exchanged RR states. We compute, in particular, the leading term of the amplitude at large distance from the branes, which corresponds to taking a field theory limit. This seems to suggest that the process takes place through the coupling of an axion to the RR states exchanged between the 0-branes. |
1207.4037 | Simone Giacomelli | Simone Giacomelli | Singular points in N=2 SQCD | 22 pages, 2 figures | null | 10.1007/JHEP09(2012)040 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We revisit the study of singular points in N=2 SQCD with classical gauge
groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa
we find that the low-energy physics at the maximally singular point involves
two superconformal sectors coupled to an infrared free SU(2) gauge group. When
one softly breaks extended supersymmetry to N=1 adding a mass term for the
chiral multiplet in the adjoint representation, a finite number of vacua remain
and the theory becomes confining. Our analysis allows to identify the
low-energy physics at these distinguished points in the moduli space. In some
cases, which we will describe in detail, two sectors coupled to an infrared
free SU(2) gauge group emerge as before. For USp and SO gauge groups one of
these sectors is always free, contrary to the SU case.
| [
{
"created": "Tue, 17 Jul 2012 15:50:45 GMT",
"version": "v1"
}
] | 2015-06-05 | [
[
"Giacomelli",
"Simone",
""
]
] | We revisit the study of singular points in N=2 SQCD with classical gauge groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa we find that the low-energy physics at the maximally singular point involves two superconformal sectors coupled to an infrared free SU(2) gauge group. When one softly breaks extended supersymmetry to N=1 adding a mass term for the chiral multiplet in the adjoint representation, a finite number of vacua remain and the theory becomes confining. Our analysis allows to identify the low-energy physics at these distinguished points in the moduli space. In some cases, which we will describe in detail, two sectors coupled to an infrared free SU(2) gauge group emerge as before. For USp and SO gauge groups one of these sectors is always free, contrary to the SU case. |
1603.06231 | Emil Nissimov | Eduardo Guendelman, Emil Nissimov and Svetlana Pacheva | Gravity-Assisted Emergent Higgs Mechanism in the Post-Inflationary Epoch | v.2 10 pages, Honorable Mention in the Gravity Research Foundation
Essay Competition 2016
(http://www.gravityresearchfoundation.org/pdf/2016_Awards.pdf), to appear in
International Journal of Modern Physics D (2016) | International Journal of Modern Physics D25 (2016) 1644008 | 10.1142/S0218271816440089 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider a non-standard model of gravity coupled to a neutral scalar
"inflaton" as well as to SU(2)xU(1) iso-doublet scalar with positive mass
squared and without self-interaction, and to SU(2)xU(1) gauge fields. The
principal new ingredient is employing two alternative non-Riemannian space-time
volume-forms (covariant integration measure densitities) independent of the
metric. The latter have a remarkable impact - although not introducing any
additional propagating degrees of freedom, their dynamics triggers a series of
important features: appearance of infinitely large flat regions of the
effective "inflaton" potential as well as dynamical generation of Higgs-like
spontaneous symmetry breaking effective potential for the SU(2)xU(1)
iso-doublet scalar.
| [
{
"created": "Sun, 20 Mar 2016 15:46:05 GMT",
"version": "v1"
},
{
"created": "Mon, 1 Aug 2016 12:59:46 GMT",
"version": "v2"
}
] | 2016-09-23 | [
[
"Guendelman",
"Eduardo",
""
],
[
"Nissimov",
"Emil",
""
],
[
"Pacheva",
"Svetlana",
""
]
] | We consider a non-standard model of gravity coupled to a neutral scalar "inflaton" as well as to SU(2)xU(1) iso-doublet scalar with positive mass squared and without self-interaction, and to SU(2)xU(1) gauge fields. The principal new ingredient is employing two alternative non-Riemannian space-time volume-forms (covariant integration measure densitities) independent of the metric. The latter have a remarkable impact - although not introducing any additional propagating degrees of freedom, their dynamics triggers a series of important features: appearance of infinitely large flat regions of the effective "inflaton" potential as well as dynamical generation of Higgs-like spontaneous symmetry breaking effective potential for the SU(2)xU(1) iso-doublet scalar. |
1012.3401 | Michael Kiermaier | Henriette Elvang, Daniel Z. Freedman, Michael Kiermaier | SUSY Ward identities, Superamplitudes, and Counterterms | 33 pages. Invited review for a special issue of Journal of Physics A
devoted to "Scattering Amplitudes in Gauge Theories." v2: references added | null | 10.1088/1751-8113/44/45/454009 | MCTP-10-56, MIT-CTP-4197, PUPT-2361 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Ward identities of SUSY and R-symmetry relate n-point amplitudes in
supersymmetric theories. We review recent work in which these Ward identities
are solved in N=4 SYM and N=8 supergravity. The solution, valid at both tree
and loop level, expresses any (Next-to)^K MHV superamplitude in terms of a
basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard
tableaux of rectangular N-by-K Young diagrams. The SUSY Ward identities also
impose constraints on the matrix elements of candidate ultraviolet counterterms
in N=8 supergravity, and they can be studied using superamplitude basis
expansions. This leads to a novel and quite comprehensive matrix element
approach to counterterms, which we also review. This article is an invited
review for a special issue of Journal of Physics A devoted to "Scattering
Amplitudes in Gauge Theories".
| [
{
"created": "Wed, 15 Dec 2010 17:53:34 GMT",
"version": "v1"
},
{
"created": "Wed, 6 Jul 2011 16:50:01 GMT",
"version": "v2"
}
] | 2015-05-20 | [
[
"Elvang",
"Henriette",
""
],
[
"Freedman",
"Daniel Z.",
""
],
[
"Kiermaier",
"Michael",
""
]
] | Ward identities of SUSY and R-symmetry relate n-point amplitudes in supersymmetric theories. We review recent work in which these Ward identities are solved in N=4 SYM and N=8 supergravity. The solution, valid at both tree and loop level, expresses any (Next-to)^K MHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard tableaux of rectangular N-by-K Young diagrams. The SUSY Ward identities also impose constraints on the matrix elements of candidate ultraviolet counterterms in N=8 supergravity, and they can be studied using superamplitude basis expansions. This leads to a novel and quite comprehensive matrix element approach to counterterms, which we also review. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories". |
hep-th/9303169 | null | Yoav Peleg | The Wave Function of a Collapsing Star and Quantization Conditions | 13 pages, BRX-TH-342 | null | null | null | hep-th | null | A very simple minisuperspace describing the Oppenheimer-Snyder collapsing
star is found. The semiclasical wave function of that model turn out to
describe a bound state. For fixed initial radius of the collapsing star, the
corrssponding Bohr-Sommerfeld quantization condition implies mass quantization.
An extension of this model, and some consequences, are considered.
| [
{
"created": "Tue, 30 Mar 1993 16:50:00 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Peleg",
"Yoav",
""
]
] | A very simple minisuperspace describing the Oppenheimer-Snyder collapsing star is found. The semiclasical wave function of that model turn out to describe a bound state. For fixed initial radius of the collapsing star, the corrssponding Bohr-Sommerfeld quantization condition implies mass quantization. An extension of this model, and some consequences, are considered. |
2407.11129 | Sungjoon Kim | Chiung Hwang, Sungjoon Kim | S-confinement of 3d Argyres-Douglas theories and the Seiberg-like
duality with an adjoint matter | 54 pages | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We propose an $\mathcal{N}=2$ preserving deformation that leads to the
confining phase of the 3d reduction of the $D_p[SU(N)]$ Argyres-Douglas
theories, referred to as $\mathbb{D}_p[SU(N)]$. This deformation incorporates
monopole superpotential terms, which have recently played interesting roles in
exploring possible RG fixed points of 3d supersymmetric gauge theories.
Employing this confining phenomenon in 3d $\mathbb{D}_p[SU(N)]$ theories, we
also propose a deconfined version of the Kim-Park duality, an IR duality for 3d
$\mathcal{N}=2$ adjoint SQCDs, where an adjoint matter field is replaced by a
linear quiver tail of $\mathbb{D}_p[SU(N)]$. Surprisingly, both the confinement
of deformed $\mathbb{D}_p[SU(N)]$ and the deconfined Kim-Park duality can be
proven only assuming some basic 3d $\mathcal{N}=2$ IR dualities. Finally, we
propose a variant of the Kim-Park duality deformed by a single monopole
superpotential term, which can also be derived using the same method.
| [
{
"created": "Mon, 15 Jul 2024 18:00:04 GMT",
"version": "v1"
}
] | 2024-07-17 | [
[
"Hwang",
"Chiung",
""
],
[
"Kim",
"Sungjoon",
""
]
] | We propose an $\mathcal{N}=2$ preserving deformation that leads to the confining phase of the 3d reduction of the $D_p[SU(N)]$ Argyres-Douglas theories, referred to as $\mathbb{D}_p[SU(N)]$. This deformation incorporates monopole superpotential terms, which have recently played interesting roles in exploring possible RG fixed points of 3d supersymmetric gauge theories. Employing this confining phenomenon in 3d $\mathbb{D}_p[SU(N)]$ theories, we also propose a deconfined version of the Kim-Park duality, an IR duality for 3d $\mathcal{N}=2$ adjoint SQCDs, where an adjoint matter field is replaced by a linear quiver tail of $\mathbb{D}_p[SU(N)]$. Surprisingly, both the confinement of deformed $\mathbb{D}_p[SU(N)]$ and the deconfined Kim-Park duality can be proven only assuming some basic 3d $\mathcal{N}=2$ IR dualities. Finally, we propose a variant of the Kim-Park duality deformed by a single monopole superpotential term, which can also be derived using the same method. |
hep-th/0411028 | Thomas Larsson | T. A. Larsson | Manifestly covariant canonical quantization I: the free scalar field | null | null | null | null | hep-th | null | Classical physics is reformulated as a constrained Hamiltonian system in the
history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role
of first-class constraints. This allows us to apply standard methods from the
theory of constrained Hamiltonian systems, e.g. Dirac brackets and
cohomological methods. In analogy with BRST quantization, we quantize in the
history phase space first and impose dynamics afterwards. To obtain a truly
covariant formulation, all fields must be expanded in a Taylor series around
the observer's trajectory, which acquires the status of a quantized physical
field. The formalism is applied to the harmonic oscillator and to the free
scalar field. Standard results are recovered, but only in the approximation
that the observer's trajectory is treated as a classical curve.
| [
{
"created": "Tue, 2 Nov 2004 11:32:49 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Larsson",
"T. A.",
""
]
] | Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the theory of constrained Hamiltonian systems, e.g. Dirac brackets and cohomological methods. In analogy with BRST quantization, we quantize in the history phase space first and impose dynamics afterwards. To obtain a truly covariant formulation, all fields must be expanded in a Taylor series around the observer's trajectory, which acquires the status of a quantized physical field. The formalism is applied to the harmonic oscillator and to the free scalar field. Standard results are recovered, but only in the approximation that the observer's trajectory is treated as a classical curve. |
1109.0471 | Jerome P. Gauntlett | Aristomenis Donos, Jerome P. Gauntlett and Christiana Pantelidou | Spatially modulated instabilities of magnetic black branes | 21 pages, 2 figures. Very minor typos fixed. Version published in
JHEP | null | 10.1007/JHEP01(2012)061 | Imperial/TP/2011/JG/05 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We investigate spatially modulated instabilities of magnetically charged
$AdS_{2}\times\mathbb{R}^2$, $AdS_{3}\times\mathbb{R}^2$ and
$AdS_{2}\times\mathbb{R}^3$ backgrounds in a broad class of theories, including
those arising from KK reductions of ten and eleven dimensional supergravity. We
show that magnetically charged black brane solutions in D=4,5 spacetime
dimensions, whose zero temperature near horizon limit approach these
backgrounds, can have instabilities that are dual to phases with current
density waves that spontaneously break translation symmetry. Our examples
include spatially modulated instabilities for a new class of magnetic black
brane solutions of D=5 SO(6) gauged supergravity, that we construct in closed
form, which are dual to new phases of N=4 SYM theory.
| [
{
"created": "Fri, 2 Sep 2011 15:10:18 GMT",
"version": "v1"
},
{
"created": "Fri, 21 Oct 2011 15:56:13 GMT",
"version": "v2"
},
{
"created": "Thu, 12 Jan 2012 16:59:24 GMT",
"version": "v3"
}
] | 2015-05-30 | [
[
"Donos",
"Aristomenis",
""
],
[
"Gauntlett",
"Jerome P.",
""
],
[
"Pantelidou",
"Christiana",
""
]
] | We investigate spatially modulated instabilities of magnetically charged $AdS_{2}\times\mathbb{R}^2$, $AdS_{3}\times\mathbb{R}^2$ and $AdS_{2}\times\mathbb{R}^3$ backgrounds in a broad class of theories, including those arising from KK reductions of ten and eleven dimensional supergravity. We show that magnetically charged black brane solutions in D=4,5 spacetime dimensions, whose zero temperature near horizon limit approach these backgrounds, can have instabilities that are dual to phases with current density waves that spontaneously break translation symmetry. Our examples include spatially modulated instabilities for a new class of magnetic black brane solutions of D=5 SO(6) gauged supergravity, that we construct in closed form, which are dual to new phases of N=4 SYM theory. |
1001.3158 | Oliver Schlotterer | Oliver Schlotterer | Higher Loop Spin Field Correlators in D=4 Superstring Theory | 59 pages, 1 figure; v2: final version published in JHEP | JHEP 1009:050,2010 | 10.1007/JHEP09(2010)050 | MPP-2009-197 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We develop calculational tools to determine higher loop superstring
correlators involving massless fermionic and spin fields in four space time
dimensions. These correlation functions are basic ingredients for the
calculation of loop amplitudes involving both bosons and fermions in D=4
heterotic and superstring theories. To obtain the full amplitudes in Lorentz
covariant form the loop correlators of fermionic and spin fields have to be
expressed in terms of SO(1,3) tensors. This is one of the main achievements in
this work.
| [
{
"created": "Tue, 19 Jan 2010 20:03:37 GMT",
"version": "v1"
},
{
"created": "Thu, 4 Nov 2010 18:48:40 GMT",
"version": "v2"
}
] | 2010-11-05 | [
[
"Schlotterer",
"Oliver",
""
]
] | We develop calculational tools to determine higher loop superstring correlators involving massless fermionic and spin fields in four space time dimensions. These correlation functions are basic ingredients for the calculation of loop amplitudes involving both bosons and fermions in D=4 heterotic and superstring theories. To obtain the full amplitudes in Lorentz covariant form the loop correlators of fermionic and spin fields have to be expressed in terms of SO(1,3) tensors. This is one of the main achievements in this work. |
1805.08977 | Mohammad R. Garousi | Mohammad R. Garousi | $O(D,D)$-constraint on $D$-dimensional effective actions | 18 pages, Latex file, no figure; v2: field redefinitions between 2D-
and D-dimensional actions are added,v3: the version appears in PRD | Phys. Rev. D 98, 066008 (2018) | 10.1103/PhysRevD.98.066008 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Double Field Theory is a manifestly T-duality invariant formulation of string
theory in which the effective theory at any order of $\alpha'$ is invariant
under global $O(D,D)$ transformations and ought to be invariant under gauge
transformations which receive $\alpha'$-corrections. On the other hand, the
effective theory in the usual $D$-dimensional formulation of string theory is
manifestly gauge invariant and ought to be invariant under T-duality
transformations which receive $\alpha'$-corrections. We speculate that the
combination of these two constraints may fix both the $2D$-dimensional and the
$D$-dimensional effective actions without knowledge of the
$\alpha'$-corrections of the gauge and the T-duality transformations.
In this paper, using generalized fluxes, we construct arbitrary
$O(D,D)$-invariant actions at orders $\alpha'^0$ and $\alpha'$, and then
dimensionally reduce them to the $D$-dimensional spacetime. On the other hand,
at these orders, we construct arbitrary covariant $D$-dimensional actions.
Constraining the two $D$-dimensional actions to be equal up to non-covariant
field redefinitions, we find that both actions are fixed up to overall factors
and up to field redefinitions.
| [
{
"created": "Wed, 23 May 2018 06:33:37 GMT",
"version": "v1"
},
{
"created": "Wed, 30 May 2018 07:59:23 GMT",
"version": "v2"
},
{
"created": "Thu, 6 Sep 2018 03:45:05 GMT",
"version": "v3"
}
] | 2018-09-19 | [
[
"Garousi",
"Mohammad R.",
""
]
] | Double Field Theory is a manifestly T-duality invariant formulation of string theory in which the effective theory at any order of $\alpha'$ is invariant under global $O(D,D)$ transformations and ought to be invariant under gauge transformations which receive $\alpha'$-corrections. On the other hand, the effective theory in the usual $D$-dimensional formulation of string theory is manifestly gauge invariant and ought to be invariant under T-duality transformations which receive $\alpha'$-corrections. We speculate that the combination of these two constraints may fix both the $2D$-dimensional and the $D$-dimensional effective actions without knowledge of the $\alpha'$-corrections of the gauge and the T-duality transformations. In this paper, using generalized fluxes, we construct arbitrary $O(D,D)$-invariant actions at orders $\alpha'^0$ and $\alpha'$, and then dimensionally reduce them to the $D$-dimensional spacetime. On the other hand, at these orders, we construct arbitrary covariant $D$-dimensional actions. Constraining the two $D$-dimensional actions to be equal up to non-covariant field redefinitions, we find that both actions are fixed up to overall factors and up to field redefinitions. |
0704.1452 | Bernard de Wit | Bernard de Wit | BPS Black Holes | 23 pages, lecture notes, Strings and Branes: the present paradigm for
gauge interactions and cosmology, Cargese 2006 | Nucl.Phys.Proc.Suppl.171:16-38,2007 | 10.1016/j.nuclphysbps.2007.06.004 | ITP-UU-07/20; SPIN-07/13 | hep-th | null | The entropy of BPS black holes in four space-time dimensions is discussed
from both macroscopic and microscopic points of view.
| [
{
"created": "Wed, 11 Apr 2007 15:55:33 GMT",
"version": "v1"
}
] | 2008-11-26 | [
[
"de Wit",
"Bernard",
""
]
] | The entropy of BPS black holes in four space-time dimensions is discussed from both macroscopic and microscopic points of view. |
hep-th/0405231 | Andrei Starinets | P.Kovtun, D.T.Son and A.O.Starinets | Viscosity in Strongly Interacting Quantum Field Theories from Black Hole
Physics | 9 pages, title changed, appendix moved into the main text | Phys.Rev.Lett. 94 (2005) 111601 | 10.1103/PhysRevLett.94.111601 | INT-PUB 04-09; UW/PT 04-04 | hep-th gr-qc hep-ph | null | The ratio of shear viscosity to volume density of entropy can be used to
characterize how close a given fluid is to being perfect. Using string theory
methods, we show that this ratio is equal to a universal value of $\hbar/4\pi
k_B$ for a large class of strongly interacting quantum field theories whose
dual description involves black holes in anti--de Sitter space. We provide
evidence that this value may serve as a lower bound for a wide class of
systems, thus suggesting that black hole horizons are dual to the most ideal
fluids.
| [
{
"created": "Wed, 26 May 2004 02:04:08 GMT",
"version": "v1"
},
{
"created": "Thu, 17 Mar 2005 01:44:41 GMT",
"version": "v2"
}
] | 2007-05-23 | [
[
"Kovtun",
"P.",
""
],
[
"Son",
"D. T.",
""
],
[
"Starinets",
"A. O.",
""
]
] | The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of $\hbar/4\pi k_B$ for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti--de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids. |
hep-th/9405130 | Kenji Hamada | Ken-ji Hamada and Hiroshi Ishikawa | Non-linear Structures in Non-critical NSR String | 22 pages, Latex file, YITP/U-94-16, UT-Komaba/94-12 | Commun.Math.Phys. 176 (1996) 401-420 | 10.1007/BF02099555 | null | hep-th | null | We investigate the Ward identities of the $\W_{\infty}$ symmetry in the
super-Liouville theory coupled to the super-conformal matter of central charge
${\hat c}_M = 1-2(p-q)^2 /pq$. The theory is classified into two chiralities.
For the positive chirality, all gravitationally dressed scaling operators are
generated from the $q-1$ gravitational primaries by acting one of the ring
generators in the R-sector on them repeatedly. After fixing the normalizations
of the dressed scaling operators, we find that the Ward identities are
expressed in the form of the {\it usual} $\W_q$ algebra constraints as in the
bosonic case: $\W^{(k+1)}_n \tau =0$, $(k=1,\cdots,q-1 ;~ n \in {\bf Z}_{\geq
1-k})$, where the equations for even and odd $n$ come from the currents in the
NS- and the R-sector respectively. The non-linear terms come from the anomalous
contributions at the boundaries of moduli space. The negative chirality is
defined by interchanging the roles of $p$ and $q$. Then we get the $\W_p $
algebra constraints.
| [
{
"created": "Fri, 20 May 1994 07:03:47 GMT",
"version": "v1"
}
] | 2015-06-26 | [
[
"Hamada",
"Ken-ji",
""
],
[
"Ishikawa",
"Hiroshi",
""
]
] | We investigate the Ward identities of the $\W_{\infty}$ symmetry in the super-Liouville theory coupled to the super-conformal matter of central charge ${\hat c}_M = 1-2(p-q)^2 /pq$. The theory is classified into two chiralities. For the positive chirality, all gravitationally dressed scaling operators are generated from the $q-1$ gravitational primaries by acting one of the ring generators in the R-sector on them repeatedly. After fixing the normalizations of the dressed scaling operators, we find that the Ward identities are expressed in the form of the {\it usual} $\W_q$ algebra constraints as in the bosonic case: $\W^{(k+1)}_n \tau =0$, $(k=1,\cdots,q-1 ;~ n \in {\bf Z}_{\geq 1-k})$, where the equations for even and odd $n$ come from the currents in the NS- and the R-sector respectively. The non-linear terms come from the anomalous contributions at the boundaries of moduli space. The negative chirality is defined by interchanging the roles of $p$ and $q$. Then we get the $\W_p $ algebra constraints. |
1909.07601 | Victor Alekseev | Victor Alekseev, Andrey Morozov, Alexey Sleptsov | Interplay between symmetries of quantum 6-j symbols and the eigenvalue
hypothesis | 22 pages | Lett Math Phys 111, 50 (2021) | 10.1007/s11005-021-01386-1 | null | hep-th math.QA math.RT | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The eigenvalue hypothesis claims that any quantum Racah matrix for
finite-dimensional representations of $U_q(sl_N)$ is uniquely determined by
eigenvalues of the corresponding quantum $\cal{R}$-matrices. If this hypothesis
turns out to be true, then it will significantly simplify the computation of
Racah matrices. Also due to this hypothesis various interesting properties of
colored HOMFLY-PT polynomials will be proved. In addition, it allows one to
discover new symmetries of the quantum 6-j symbols, about which almost nothing
is known for $N>2$, with the exception of the tetrahedral symmetries, complex
conjugation and transformation $q \longleftrightarrow q^{-1}$.
In this paper we prove the eigenvalue hypothesis in $U_q(sl_2)$ case and show
that it is equivalent to 6-j symbol symmetries (the Regge symmetry and two
argument permutations). Then we apply the eigenvalue hypothesis to inclusive
Racah matrices with 3 symmetric incoming representations of $U_q(sl_N)$ and an
arbitrary outcoming one. It gives us 8 new additional symmetries that are not
tetrahedral ones. Finally, we apply the eigenvalue hypothesis to exclusive
Racah matrices with symmetric representations and obtain 4 tetrahedral
symmetries.
| [
{
"created": "Tue, 17 Sep 2019 05:45:40 GMT",
"version": "v1"
},
{
"created": "Tue, 24 Sep 2019 07:58:19 GMT",
"version": "v2"
},
{
"created": "Sun, 29 Mar 2020 14:58:55 GMT",
"version": "v3"
},
{
"created": "Sat, 8 Aug 2020 19:36:27 GMT",
"version": "v4"
},
{
"created": "Wed, 19 Aug 2020 13:32:38 GMT",
"version": "v5"
},
{
"created": "Thu, 7 Jan 2021 07:57:11 GMT",
"version": "v6"
},
{
"created": "Wed, 17 Mar 2021 19:40:06 GMT",
"version": "v7"
}
] | 2021-05-04 | [
[
"Alekseev",
"Victor",
""
],
[
"Morozov",
"Andrey",
""
],
[
"Sleptsov",
"Alexey",
""
]
] | The eigenvalue hypothesis claims that any quantum Racah matrix for finite-dimensional representations of $U_q(sl_N)$ is uniquely determined by eigenvalues of the corresponding quantum $\cal{R}$-matrices. If this hypothesis turns out to be true, then it will significantly simplify the computation of Racah matrices. Also due to this hypothesis various interesting properties of colored HOMFLY-PT polynomials will be proved. In addition, it allows one to discover new symmetries of the quantum 6-j symbols, about which almost nothing is known for $N>2$, with the exception of the tetrahedral symmetries, complex conjugation and transformation $q \longleftrightarrow q^{-1}$. In this paper we prove the eigenvalue hypothesis in $U_q(sl_2)$ case and show that it is equivalent to 6-j symbol symmetries (the Regge symmetry and two argument permutations). Then we apply the eigenvalue hypothesis to inclusive Racah matrices with 3 symmetric incoming representations of $U_q(sl_N)$ and an arbitrary outcoming one. It gives us 8 new additional symmetries that are not tetrahedral ones. Finally, we apply the eigenvalue hypothesis to exclusive Racah matrices with symmetric representations and obtain 4 tetrahedral symmetries. |
hep-th/9511104 | Igor Klebanov | D. J. Gross, I. R. Klebanov, A. V. Matytsin, A. V. Smilga | Screening vs. Confinement in 1+1 Dimensions | 29 pages, latex, no figures. slight change in the wording on page 2,
references added | Nucl.Phys. B461 (1996) 109-130 | 10.1016/0550-3213(95)00655-9 | PUPT-1577, CTP-2487 | hep-th hep-ph | null | We show that, in 1+1 dimensional gauge theories, a heavy probe charge is
screened by dynamical massless fermions both in the case when the source and
the dynamical fermions belong to the same representation of the gauge group
and, unexpectedly, in the case when the representation of the probe charge is
smaller than the representation of the massless fermions. Thus, a fractionally
charged heavy probe is screened by dynamical fermions of integer charge in the
massless Schwinger model, and a colored probe in the fundamental representation
is screened in $QCD_2$ with adjoint massless Majorana fermions. The screening
disappears and confinement is restored as soon as the dynamical fermions are
given a non-zero mass. For small masses, the string tension is given by the
product of the light fermion mass and the fermion condensate with a known
numerical coefficient. Parallels with 3+1 dimensional $QCD$ and supersymmetric
gauge theories are discussed.
| [
{
"created": "Tue, 14 Nov 1995 23:01:44 GMT",
"version": "v1"
},
{
"created": "Thu, 16 Nov 1995 21:27:06 GMT",
"version": "v2"
}
] | 2009-10-28 | [
[
"Gross",
"D. J.",
""
],
[
"Klebanov",
"I. R.",
""
],
[
"Matytsin",
"A. V.",
""
],
[
"Smilga",
"A. V.",
""
]
] | We show that, in 1+1 dimensional gauge theories, a heavy probe charge is screened by dynamical massless fermions both in the case when the source and the dynamical fermions belong to the same representation of the gauge group and, unexpectedly, in the case when the representation of the probe charge is smaller than the representation of the massless fermions. Thus, a fractionally charged heavy probe is screened by dynamical fermions of integer charge in the massless Schwinger model, and a colored probe in the fundamental representation is screened in $QCD_2$ with adjoint massless Majorana fermions. The screening disappears and confinement is restored as soon as the dynamical fermions are given a non-zero mass. For small masses, the string tension is given by the product of the light fermion mass and the fermion condensate with a known numerical coefficient. Parallels with 3+1 dimensional $QCD$ and supersymmetric gauge theories are discussed. |
2312.11634 | Ashoke Sen | Ashoke Sen | String Theory in Rolling Tachyon Vacuum | LaTeX, 23 pages; v2: references added | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We suggest that the universe filled with unstable D-branes in their rolling
tachyon vacuum state, described by periodic arrays of D-instantons along the
imaginary time direction, may be a natural background for formulating string
theory. While the presence of these D-instanton arrays do not affect the usual
perturbative closed string amplitudes, the open string degrees of freedom on
the instanton may be used to create the regular D-branes via a series of
marginal deformations, thereby describing D-branes as regular classical
solutions in the theory. Furthermore, we argue that a combination of the open
string degrees of freedom in the rolling tachyon vacuum is set equal to time by
the equations of motion, and hence this combination could provide an intrinsic
definition of time in the theory. We illustrate these observations using the
example of two dimensional string theory.
| [
{
"created": "Mon, 18 Dec 2023 19:00:04 GMT",
"version": "v1"
},
{
"created": "Thu, 21 Dec 2023 05:07:46 GMT",
"version": "v2"
}
] | 2023-12-22 | [
[
"Sen",
"Ashoke",
""
]
] | We suggest that the universe filled with unstable D-branes in their rolling tachyon vacuum state, described by periodic arrays of D-instantons along the imaginary time direction, may be a natural background for formulating string theory. While the presence of these D-instanton arrays do not affect the usual perturbative closed string amplitudes, the open string degrees of freedom on the instanton may be used to create the regular D-branes via a series of marginal deformations, thereby describing D-branes as regular classical solutions in the theory. Furthermore, we argue that a combination of the open string degrees of freedom in the rolling tachyon vacuum is set equal to time by the equations of motion, and hence this combination could provide an intrinsic definition of time in the theory. We illustrate these observations using the example of two dimensional string theory. |
2204.10334 | Edward Hirst | Jiakang Bao, Yang-Hui He, Elli Heyes, Edward Hirst | Machine Learning Algebraic Geometry for Physics | 32 pages, 25 figures. Contribution to Machine learning and Algebraic
Geometry, edited by A. Kasprzyk et al | null | null | LIMS-2022-012 | hep-th math.AG stat.ML | http://creativecommons.org/publicdomain/zero/1.0/ | We review some recent applications of machine learning to algebraic geometry
and physics. Since problems in algebraic geometry can typically be reformulated
as mappings between tensors, this makes them particularly amenable to
supervised learning. Additionally, unsupervised methods can provide insight
into the structure of such geometrical data. At the heart of this programme is
the question of how geometry can be machine learned, and indeed how AI helps
one to do mathematics. This is a chapter contribution to the book Machine
learning and Algebraic Geometry, edited by A. Kasprzyk et al.
| [
{
"created": "Thu, 21 Apr 2022 18:00:03 GMT",
"version": "v1"
}
] | 2022-04-25 | [
[
"Bao",
"Jiakang",
""
],
[
"He",
"Yang-Hui",
""
],
[
"Heyes",
"Elli",
""
],
[
"Hirst",
"Edward",
""
]
] | We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised learning. Additionally, unsupervised methods can provide insight into the structure of such geometrical data. At the heart of this programme is the question of how geometry can be machine learned, and indeed how AI helps one to do mathematics. This is a chapter contribution to the book Machine learning and Algebraic Geometry, edited by A. Kasprzyk et al. |
hep-th/0609182 | Bouatta Nazim | L. Bonora, N. Bouatta and C. Maccaferri | Towards open-closed string duality: Closed Strings as Open String Fields | 29 pages | null | null | null | hep-th | null | We establish a translation dictionary between open and closed strings,
starting from open string field theory. Under this correspondence, (off-shell)
level-matched closed string states are represented by star algebra projectors
in open string field theory. Particular attention is paid to the zero mode
sector, which is indispensable in order to generate closed string states with
momentum. As an outcome of our identification, we show that boundary states,
which in closed string theory represent D-branes, correspond to the identity
string field in the open string side. It is to be remarked that closed string
theory D-branes are thus given by an infinite superposition of star algebra
projectors.
| [
{
"created": "Tue, 26 Sep 2006 15:08:07 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Bonora",
"L.",
""
],
[
"Bouatta",
"N.",
""
],
[
"Maccaferri",
"C.",
""
]
] | We establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, (off-shell) level-matched closed string states are represented by star algebra projectors in open string field theory. Particular attention is paid to the zero mode sector, which is indispensable in order to generate closed string states with momentum. As an outcome of our identification, we show that boundary states, which in closed string theory represent D-branes, correspond to the identity string field in the open string side. It is to be remarked that closed string theory D-branes are thus given by an infinite superposition of star algebra projectors. |
1307.1802 | Caio Costa | Caio V. Costa, Dmitry M. Gitman and Anatoly E. Shabad | Nonlinear corrections in basic problems of electro- and magneto-statics
in the vacuum | 21 pages, 1 figure | Phys. Rev. D 88, 085026 (2013) | 10.1103/PhysRevD.88.085026 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We find third-power nonlinear corrections to the Coulomb and other static
electric fields, as well as to the electric and magnetic dipole fields, as we
work within QED with no background field. The nonlinear response function we
base our consideration on is the fourth-rank polarization tensor, calculated
within the local (infrared) approximation of the effective action. Therefore,
the results are applicable to weakly varying fields. It is established that the
nonlinear correction to magnetic moment of some baryons just matches, in the
order of magnitude, the existing gap between its experimental and theoretical
values.
| [
{
"created": "Sat, 6 Jul 2013 18:19:26 GMT",
"version": "v1"
},
{
"created": "Tue, 9 Jul 2013 16:26:37 GMT",
"version": "v2"
}
] | 2013-10-30 | [
[
"Costa",
"Caio V.",
""
],
[
"Gitman",
"Dmitry M.",
""
],
[
"Shabad",
"Anatoly E.",
""
]
] | We find third-power nonlinear corrections to the Coulomb and other static electric fields, as well as to the electric and magnetic dipole fields, as we work within QED with no background field. The nonlinear response function we base our consideration on is the fourth-rank polarization tensor, calculated within the local (infrared) approximation of the effective action. Therefore, the results are applicable to weakly varying fields. It is established that the nonlinear correction to magnetic moment of some baryons just matches, in the order of magnitude, the existing gap between its experimental and theoretical values. |
hep-th/9207118 | Itzhak Bars | Itzhak Bars | Heterotic String Models in Curved Spacetime | USC-92/HEP-B4, 10 pages | Phys.Lett.B293:315-320,1992 | 10.1016/0370-2693(92)90889-C | null | hep-th hep-ph | null | We explore the possibility of string theories in only four spacetime
dimensions without any additional compactified dimensions. We show that,
provided the theory is defined in curved spacetime that has a cosmological
interpration, it is possible to construct consistent heterotic string theories
based on a few non-compact current algebra cosets. We classify these models.
The gauge groups that emerge fall within a remarkably narrow range and include
the desirable low energy flavor symmetry of $SU(3)\times SU(2)\times U(1)$. The
quark and lepton states, which come in color triplets and $SU(2)$ doublets, are
expected to emerge in several families.
| [
{
"created": "Sat, 1 Aug 1992 06:04:18 GMT",
"version": "v1"
}
] | 2008-11-26 | [
[
"Bars",
"Itzhak",
""
]
] | We explore the possibility of string theories in only four spacetime dimensions without any additional compactified dimensions. We show that, provided the theory is defined in curved spacetime that has a cosmological interpration, it is possible to construct consistent heterotic string theories based on a few non-compact current algebra cosets. We classify these models. The gauge groups that emerge fall within a remarkably narrow range and include the desirable low energy flavor symmetry of $SU(3)\times SU(2)\times U(1)$. The quark and lepton states, which come in color triplets and $SU(2)$ doublets, are expected to emerge in several families. |
1106.2967 | Johannes Walcher | Shmuel Elitzur, Yaron Oz, Eliezer Rabinovici, Johannes Walcher | Open/Closed Topological CP1 Sigma Model Revisited | 25 pages | null | 10.1007/JHEP01(2012)101 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider the topological sigma-model on Riemann surfaces with genus g and
h holes, and target space CP1. We calculate the correlation functions of bulk
and boundary operators, and study the symmetries of the model and its most
general deformation. We study the open/closed topological field theory (TFT)
correspondence by summing up the boundaries. We argue that this summation can
be understood as a renormalization of the closed TFT. We couple the model to
topological gravity and derive constitutive relations between the correlation
functions of bulk and boundary operators.
| [
{
"created": "Wed, 15 Jun 2011 13:18:21 GMT",
"version": "v1"
},
{
"created": "Mon, 21 Nov 2011 15:17:58 GMT",
"version": "v2"
}
] | 2015-05-28 | [
[
"Elitzur",
"Shmuel",
""
],
[
"Oz",
"Yaron",
""
],
[
"Rabinovici",
"Eliezer",
""
],
[
"Walcher",
"Johannes",
""
]
] | We consider the topological sigma-model on Riemann surfaces with genus g and h holes, and target space CP1. We calculate the correlation functions of bulk and boundary operators, and study the symmetries of the model and its most general deformation. We study the open/closed topological field theory (TFT) correspondence by summing up the boundaries. We argue that this summation can be understood as a renormalization of the closed TFT. We couple the model to topological gravity and derive constitutive relations between the correlation functions of bulk and boundary operators. |
hep-th/9511043 | Constantin Bachas | C. Bachas (ITP, Ecole Polytechnique) | D-brane dynamics | 11 pages, latex. References and some extra comments added | Phys.Lett.B374:37-42,1996 | 10.1016/0370-2693(96)00238-9 | NSF-ITP/95-144 and CPTH-S388.1195 | hep-th | null | I calculate the semiclassical phase shift ($\delta$), as function of impact
parameter ($b$) and velocity ($v$), when one D-brane moves past another. From
its low-velocity expansion I show that, for torroidal compactifications, the
moduli space of two identical D-branes stays flat to all orders in
$\alpha^\prime$. For K3 compactifications, the calculation of the D-brane
moduli-space metric can be mapped to a dual gauge-coupling renormalization
problem. In the ultrarelativistic regime, the absorptive part of the phase
shift grows as if the D-branes were black disks of area $\sim \alpha^\prime
ln{1\over 1-v^2}$. The scattering of large fundamental strings shares all the
above qualitative features. A side remark concerns the intriguing duality
between limiting electric fields and the speed of light.
| [
{
"created": "Tue, 7 Nov 1995 06:20:21 GMT",
"version": "v1"
},
{
"created": "Fri, 22 Dec 1995 17:38:46 GMT",
"version": "v2"
}
] | 2010-11-19 | [
[
"Bachas",
"C.",
"",
"ITP, Ecole Polytechnique"
]
] | I calculate the semiclassical phase shift ($\delta$), as function of impact parameter ($b$) and velocity ($v$), when one D-brane moves past another. From its low-velocity expansion I show that, for torroidal compactifications, the moduli space of two identical D-branes stays flat to all orders in $\alpha^\prime$. For K3 compactifications, the calculation of the D-brane moduli-space metric can be mapped to a dual gauge-coupling renormalization problem. In the ultrarelativistic regime, the absorptive part of the phase shift grows as if the D-branes were black disks of area $\sim \alpha^\prime ln{1\over 1-v^2}$. The scattering of large fundamental strings shares all the above qualitative features. A side remark concerns the intriguing duality between limiting electric fields and the speed of light. |
1602.00337 | Ruben Mkrtchyan | H.M.Khudaverdian and R.L.Mkrtchyan | Universal volume of groups and anomaly of Vogel's symmetry | 28 pages | null | 10.1007/s11005-017-0949-8 | null | hep-th math-ph math.GR math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We show that integral representation of universal volume function of compact
simple Lie groups gives rise to six analytic functions on $CP^2$, which
transform as two triplets under group of permutations of Vogel's projective
parameters. This substitutes expected invariance under permutations of
universal parameters by more complicated covariance. We provide an analytical
continuation of these functions and particularly calculate their change under
permutations of parameters. This last relation is universal generalization, for
an arbitrary simple Lie group and an arbitrary point in Vogel's plane, of the
Kinkelin's reflection relation on Barnes' $G(1+N)$ function. Kinkelin's
relation gives asymmetry of the $G(1+N)$ function (which is essentially the
volume function for $SU(N)$ groups) under $N\leftrightarrow -N$ transformation
(which is equivalent of the permutation of parameters, for $SU(N)$ groups), and
coincides with universal relation on permutations at the $SU(N)$ line on
Vogel's plane. These results are also applicable to universal partition
function of Chern-Simons theory on three-dimensional sphere. This effect is
analogous to modular covariance, instead of invariance, of partition functions
of appropriate gauge theories under modular transformation of couplings.
| [
{
"created": "Sun, 31 Jan 2016 22:54:06 GMT",
"version": "v1"
}
] | 2017-04-05 | [
[
"Khudaverdian",
"H. M.",
""
],
[
"Mkrtchyan",
"R. L.",
""
]
] | We show that integral representation of universal volume function of compact simple Lie groups gives rise to six analytic functions on $CP^2$, which transform as two triplets under group of permutations of Vogel's projective parameters. This substitutes expected invariance under permutations of universal parameters by more complicated covariance. We provide an analytical continuation of these functions and particularly calculate their change under permutations of parameters. This last relation is universal generalization, for an arbitrary simple Lie group and an arbitrary point in Vogel's plane, of the Kinkelin's reflection relation on Barnes' $G(1+N)$ function. Kinkelin's relation gives asymmetry of the $G(1+N)$ function (which is essentially the volume function for $SU(N)$ groups) under $N\leftrightarrow -N$ transformation (which is equivalent of the permutation of parameters, for $SU(N)$ groups), and coincides with universal relation on permutations at the $SU(N)$ line on Vogel's plane. These results are also applicable to universal partition function of Chern-Simons theory on three-dimensional sphere. This effect is analogous to modular covariance, instead of invariance, of partition functions of appropriate gauge theories under modular transformation of couplings. |
1802.06618 | Mohammad Asadi | Mohammad Asadi, Reza Fareghbal | Holographic Calculation of BMSFT Mutual and 3-partite Information | 15 pages | null | 10.1140/epjc/s10052-018-6098-0 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We use flat-space holography to calculate the mutual information and the
3-partite information of a two-dimensional BMS-invariant field theory
(BMSFT$_2$). This theory is the putative holographic dual of the
three-dimensional asymptotically flat spacetimes. We find a bound in which
entangling transition occurs for zero and finite temperature BMSFTs. We also
show that the holographic 3-partite information is always non-positive which
indicates that the holographic mutual information is monogamous.
| [
{
"created": "Mon, 19 Feb 2018 13:06:55 GMT",
"version": "v1"
}
] | 2018-08-29 | [
[
"Asadi",
"Mohammad",
""
],
[
"Fareghbal",
"Reza",
""
]
] | We use flat-space holography to calculate the mutual information and the 3-partite information of a two-dimensional BMS-invariant field theory (BMSFT$_2$). This theory is the putative holographic dual of the three-dimensional asymptotically flat spacetimes. We find a bound in which entangling transition occurs for zero and finite temperature BMSFTs. We also show that the holographic 3-partite information is always non-positive which indicates that the holographic mutual information is monogamous. |
0904.1936 | Noriaki Ikeda | Noriaki Ikeda and Takeshi Fukuyama | Fermions in (Anti) de Sitter Gravity in Four Dimensions | 18 pages | Prog.Theor.Phys.122:339-353,2009 | 10.1143/PTP.122.339 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Fermions in (anti) de Sitter gravity theory in four dimensions are
considered. Especially we propose new fermion actions to derive a Weyl or
Majorana fermion action if we break the AdS (dS) group to the Lorentz group in
curved spacetime.
| [
{
"created": "Mon, 13 Apr 2009 09:39:14 GMT",
"version": "v1"
},
{
"created": "Wed, 15 Apr 2009 06:12:36 GMT",
"version": "v2"
},
{
"created": "Thu, 21 May 2009 02:21:56 GMT",
"version": "v3"
}
] | 2009-11-19 | [
[
"Ikeda",
"Noriaki",
""
],
[
"Fukuyama",
"Takeshi",
""
]
] | Fermions in (anti) de Sitter gravity theory in four dimensions are considered. Especially we propose new fermion actions to derive a Weyl or Majorana fermion action if we break the AdS (dS) group to the Lorentz group in curved spacetime. |
2407.15090 | Netanel Barel Mr. | Netanel Barel | Correlation Functions in $\textrm{T}\bar{\textrm{T}}$-deformed Theories
on the Torus | 25 pages + appendices, 7 figures. v2: slight modifications | null | null | null | hep-th | http://creativecommons.org/licenses/by/4.0/ | We study the correlation functions of local operators in unitary
$\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a torus, using
their formulation in terms of Jackiw-Teitelboim gravity. We focus on the
two-point correlation function in momentum space when the undeformed theory is
a conformal field theory. The large momentum behavior of the correlation
function is computed and compared to that of
$\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a plane. For
the latter, the behavior found was $|q|^{-\frac{tq^2}{\pi}}$, where $q$ is the
momentum and $t$ is the deformation parameter. For a torus, the same behavior
is found for $|q|<<L/t$, where $L$ is the torus' length scale. However, for
$|q|>>L/t$, a different behavior is found: $\left(\frac{4\sqrt{t}^5q^2}{\pi e
L^3|T|^2}\right)^{\frac{tq^2}{\pi}}$, where $T$ is the modular parameter of the
torus. Hence, at large momentum, the correlator decays and then grows. This
behavior suggests that operators carrying momentum $q$ are smeared on a
distance scale $t|q|$. The difference from the plane's result illustrates the
non-locality of the theory and the UV-IR mixing.
| [
{
"created": "Sun, 21 Jul 2024 08:25:24 GMT",
"version": "v1"
},
{
"created": "Thu, 1 Aug 2024 10:13:25 GMT",
"version": "v2"
}
] | 2024-08-02 | [
[
"Barel",
"Netanel",
""
]
] | We study the correlation functions of local operators in unitary $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation function in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation function is computed and compared to that of $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a plane. For the latter, the behavior found was $|q|^{-\frac{tq^2}{\pi}}$, where $q$ is the momentum and $t$ is the deformation parameter. For a torus, the same behavior is found for $|q|<<L/t$, where $L$ is the torus' length scale. However, for $|q|>>L/t$, a different behavior is found: $\left(\frac{4\sqrt{t}^5q^2}{\pi e L^3|T|^2}\right)^{\frac{tq^2}{\pi}}$, where $T$ is the modular parameter of the torus. Hence, at large momentum, the correlator decays and then grows. This behavior suggests that operators carrying momentum $q$ are smeared on a distance scale $t|q|$. The difference from the plane's result illustrates the non-locality of the theory and the UV-IR mixing. |
1501.01310 | Du Pei | Sergei Gukov and Du Pei | Equivariant Verlinde formula from fivebranes and vortices | 56 pages, 7 figures; v2: misprints corrected, clarifications added,
missing factors and terms restored in section 6.2 | null | null | CALT-TH-2014-171 | hep-th math-ph math.AG math.GT math.MP math.QA | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study complex Chern-Simons theory on a Seifert manifold $M_3$ by embedding
it into string theory. We show that complex Chern-Simons theory on $M_3$ is
equivalent to a topologically twisted supersymmetric theory and its partition
function can be naturally regularized by turning on a mass parameter. We find
that the dimensional reduction of this theory to 2d gives the low energy
dynamics of vortices in four-dimensional gauge theory, the fact apparently
overlooked in the vortex literature. We also generalize the relations between
1) the Verlinde algebra, 2) quantum cohomology of the Grassmannian, 3)
Chern-Simons theory on $\Sigma\times S^1$ and 4) index of a spin$^c$ Dirac
operator on the moduli space of flat connections to a new set of relations
between 1) the "equivariant Verlinde algebra" for a complex group, 2) the
equivariant quantum K-theory of the vortex moduli space, 3) complex
Chern-Simons theory on $\Sigma \times S^1$ and 4) the equivariant index of a
spin$^c$ Dirac operator on the moduli space of Higgs bundles.
| [
{
"created": "Tue, 6 Jan 2015 21:00:10 GMT",
"version": "v1"
},
{
"created": "Mon, 30 May 2016 22:35:36 GMT",
"version": "v2"
}
] | 2016-06-01 | [
[
"Gukov",
"Sergei",
""
],
[
"Pei",
"Du",
""
]
] | We study complex Chern-Simons theory on a Seifert manifold $M_3$ by embedding it into string theory. We show that complex Chern-Simons theory on $M_3$ is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between 1) the Verlinde algebra, 2) quantum cohomology of the Grassmannian, 3) Chern-Simons theory on $\Sigma\times S^1$ and 4) index of a spin$^c$ Dirac operator on the moduli space of flat connections to a new set of relations between 1) the "equivariant Verlinde algebra" for a complex group, 2) the equivariant quantum K-theory of the vortex moduli space, 3) complex Chern-Simons theory on $\Sigma \times S^1$ and 4) the equivariant index of a spin$^c$ Dirac operator on the moduli space of Higgs bundles. |
hep-th/0501229 | Jerome P. Gauntlett | Jerome P. Gauntlett | Classifying Supergravity Solutions | 16 pages. To appear in the Proceedings of the 37th International
Symposium Ahrenshoop, ``Recent Developments in String/M-Theory and Field
Theory", August 23-27 2004, Berlin-Schmoeckwitz. References added | Fortsch.Phys. 53 (2005) 468-479 | 10.1002/prop.200510206 | null | hep-th | null | We review the substantial progress that has been made in classifying
supersymmetric solutions of supergravity theories using G-structures. We also
review the construction of supersymmetric black rings that were discovered
using the classification of D=5 supergravity solutions.
| [
{
"created": "Fri, 28 Jan 2005 14:22:49 GMT",
"version": "v1"
},
{
"created": "Fri, 11 Feb 2005 13:35:50 GMT",
"version": "v2"
}
] | 2015-06-26 | [
[
"Gauntlett",
"Jerome P.",
""
]
] | We review the substantial progress that has been made in classifying supersymmetric solutions of supergravity theories using G-structures. We also review the construction of supersymmetric black rings that were discovered using the classification of D=5 supergravity solutions. |
hep-th/9207032 | null | A.Ch. Ganchev and V.B. Petkova | Reduction of the Knizhnik-Zamolodchikov Equation - a Way of Producing
Virasoro Algebra Singular Vectors | 12 pages, plain TeX, SISSA-111/92/EP | Phys.Lett. B293 (1992) 56-66 | 10.1016/0370-2693(92)91480-W | null | hep-th | null | It is shown that the sl(2,C) KZ equation for (half-) integer isospins
recovers, up to a gauge transformation, the matrix system for Virasoro algebra
singular vectors of Bauer et al. In the case of Kac-Kazhdan spins the general
(infinite matrix) KZ system is truncated due to the decoupling of the A^(1)_1
singular vectors. This suggests an algorithm converting Malikov-Feigin-Fuks
singular vectors into Virasoro ones.
| [
{
"created": "Fri, 10 Jul 1992 08:44:10 GMT",
"version": "v1"
}
] | 2009-10-22 | [
[
"Ganchev",
"A. Ch.",
""
],
[
"Petkova",
"V. B.",
""
]
] | It is shown that the sl(2,C) KZ equation for (half-) integer isospins recovers, up to a gauge transformation, the matrix system for Virasoro algebra singular vectors of Bauer et al. In the case of Kac-Kazhdan spins the general (infinite matrix) KZ system is truncated due to the decoupling of the A^(1)_1 singular vectors. This suggests an algorithm converting Malikov-Feigin-Fuks singular vectors into Virasoro ones. |
hep-th/9904170 | Stefan Ulrych | S. Ulrych | A second order differential equation for the relativistic description of
electrons and photons | Reverted preprint to initial version of 1999. Most of the content has
been published under the new title "Relativistic quantum physics with
hyperbolic numbers". However, interesting parts like the second quantization
of fermion fields within a Klein-Gordon theory, which is only possible with
the help of hyperbolic or bicomplex numbers, dropped out of the revised
version | Phys.Lett.B625:313-323,2005 | 10.1016/j.physletb.2005.08.072 | null | hep-th math-ph math.MP nucl-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A new relativistic description of quantum electrodynamics is presented.
Guideline of the theory is the Klein-Gordon equation, which is reformulated to
consider spin effects. This is achieved by a representation of relativistic
vectors with a space-time algebra made up of Pauli matrices and hyperbolic
numbers. The algebra is used to construct the differential operator of the
electron as well as the photon wave equation. The properties of free electron
and photon states related to this wave equation are investigated. Interactions
are introduced as usual with the minimal substitution of the momentum
operators. It can be shown that the new wave equation is equivalent to the
quadratic form of the Dirac equation. Furthermore, the Maxwell equations can be
derived from the corresponding wave equation for photons.
| [
{
"created": "Mon, 26 Apr 1999 10:27:20 GMT",
"version": "v1"
},
{
"created": "Sat, 22 Oct 2005 12:26:28 GMT",
"version": "v2"
},
{
"created": "Sun, 21 Oct 2018 09:56:27 GMT",
"version": "v3"
}
] | 2018-10-23 | [
[
"Ulrych",
"S.",
""
]
] | A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with a space-time algebra made up of Pauli matrices and hyperbolic numbers. The algebra is used to construct the differential operator of the electron as well as the photon wave equation. The properties of free electron and photon states related to this wave equation are investigated. Interactions are introduced as usual with the minimal substitution of the momentum operators. It can be shown that the new wave equation is equivalent to the quadratic form of the Dirac equation. Furthermore, the Maxwell equations can be derived from the corresponding wave equation for photons. |
hep-th/9312086 | Andrei Mikhailov | A.Mikhailov | Comultiplication in ABCD algebra and scalar products of Bethe wave
functions | 9 pages | Phys.Lett. B325 (1994) 143-148; Theor.Math.Phys. 100 (1995)
886-889 | 10.1016/0370-2693(94)90084-1 | FIAN/TD-20/93 | hep-th | null | The representation of scalar products of Bethe wave functions in terms of the
Dual Fields, proven by A.G.Izergin and V.E.Korepin in 1987, plays an important
role in the theory of completely integrable models. The proof in
\cite{Izergin87} and \cite{Korepin87} is based on the explicit expression for
the "senior" coefficient which was guessed in \cite{Izergin87} and then proven
to satisfy some recurrent relations, which determine it unambiguously. In this
paper we present an alternative proof based on the direct computation.
| [
{
"created": "Fri, 10 Dec 1993 15:19:56 GMT",
"version": "v1"
},
{
"created": "Mon, 20 Dec 1993 08:19:34 GMT",
"version": "v2"
}
] | 2009-10-22 | [
[
"Mikhailov",
"A.",
""
]
] | The representation of scalar products of Bethe wave functions in terms of the Dual Fields, proven by A.G.Izergin and V.E.Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in \cite{Izergin87} and \cite{Korepin87} is based on the explicit expression for the "senior" coefficient which was guessed in \cite{Izergin87} and then proven to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on the direct computation. |
2306.13767 | Sara Saghafi | Sara Saghafi, Kourosh Nozari | Shadow Behavior of the Quantum-Corrected Schwarzschild Black Hole
Immersed in Holographic Quintessence | 6 pages, 1 figure | Journal of Holography Applications in Physic, 2, 31-38, (2022) | 10.22128/JHAP.2022.515.1019 | null | hep-th hep-ph | http://creativecommons.org/licenses/by/4.0/ | In this paper, we aim to explore the impact of the Planck scale corrections
and the Holographic quintessence on the shadow behavior of non-rotating black
holes. To do this, we consider the quantum-corrected Schwarzschild black hole
surrounded by the quintessence field inspired by the Kazakov-Solodukhin and the
Kiselev ideas, and we call this combination the Kazakov-Solodukhin-Kiselev
(KSK) black hole. We conclude that the quintessence field as the candidate of
dark energy in the black hole can be interpreted as Holographic quintessence.
To find the geodesic equations of the black hole, we employ the Hamilton-Jacobi
approach and also, the Carter procedure. We discover that the size of the
shadow of this black hole, which depends on its central mass, is also
determined by the Planck scale effects and Holographic quintessence.
| [
{
"created": "Fri, 26 May 2023 16:39:34 GMT",
"version": "v1"
}
] | 2023-07-06 | [
[
"Saghafi",
"Sara",
""
],
[
"Nozari",
"Kourosh",
""
]
] | In this paper, we aim to explore the impact of the Planck scale corrections and the Holographic quintessence on the shadow behavior of non-rotating black holes. To do this, we consider the quantum-corrected Schwarzschild black hole surrounded by the quintessence field inspired by the Kazakov-Solodukhin and the Kiselev ideas, and we call this combination the Kazakov-Solodukhin-Kiselev (KSK) black hole. We conclude that the quintessence field as the candidate of dark energy in the black hole can be interpreted as Holographic quintessence. To find the geodesic equations of the black hole, we employ the Hamilton-Jacobi approach and also, the Carter procedure. We discover that the size of the shadow of this black hole, which depends on its central mass, is also determined by the Planck scale effects and Holographic quintessence. |
0709.1491 | Zygmunt Lalak | Zygmunt Lalak | Moduli and multi-field inflation | 8 pages, 5 figures, based on talks given at CTP Symposium on
Supersymmetry at LHC (Cairo, March 11-14 2007) and String Phenomenology 2007
(Frascati, June 4-8 2007) | Int.J.Mod.Phys.A22:5760-5770,2007 | 10.1142/S0217751X07038992 | null | hep-th | null | Moduli with flat or run-away classical potentials are generic in theories
based on supersymmetry and extra dimensions. They mix between themselves and
with matter fields in kinetic terms and in the nonperturbative superpotentials.
As the result, interesting structure appears in the scalar potential which
helps to stabilise and trap moduli and leads to multi-field inflation. The new
and attractive feature of multi-inflationary setup are isocurvature
perturbations which can modify in an interesting way the final spectrum of
primordial fluctuations resulting from inflation.
| [
{
"created": "Mon, 10 Sep 2007 21:34:54 GMT",
"version": "v1"
}
] | 2010-11-03 | [
[
"Lalak",
"Zygmunt",
""
]
] | Moduli with flat or run-away classical potentials are generic in theories based on supersymmetry and extra dimensions. They mix between themselves and with matter fields in kinetic terms and in the nonperturbative superpotentials. As the result, interesting structure appears in the scalar potential which helps to stabilise and trap moduli and leads to multi-field inflation. The new and attractive feature of multi-inflationary setup are isocurvature perturbations which can modify in an interesting way the final spectrum of primordial fluctuations resulting from inflation. |
hep-th/0407103 | Howard E. Brandt | Howard E. Brandt | Finslerian Quantum Field Theory | Invited plenary lecture at the Fourth World Congress of Nonlinear
Analysts in the session: Applications of Finsler Differential Geometry (in
Engineering, Physics and Biology), July 5, 2004, Orlando, Florida | null | null | null | hep-th gr-qc quant-ph | null | Finsler geometry motivates a generalization of the Riemannian structure of
spacetime to include dependence of the spacetime metric and associated
invariant tensor fields on the four-velocity coordinates as well as the
spacetime coordinates of the observer. It is then useful to consider the
tangent bundle of spacetime with spacetime in the base manifold and
four-velocity space in the fiber. A physical basis for the differential
geometric structure of the spacetime tangent bundle is provided by the
universal upper limit on proper acceleration relative to the vacuum. It is then
natural to consider a quantum field having a vanishing eigenvalue when acted on
by the Laplace-Beltrami operator of the spacetime tangent bundle. On this basis
a quantum field theory can be constructed having a built-in intrinsic
regularization at the Planck scale, and finite vacuum energy density.
| [
{
"created": "Tue, 13 Jul 2004 15:51:50 GMT",
"version": "v1"
},
{
"created": "Thu, 15 Jul 2004 13:34:57 GMT",
"version": "v2"
}
] | 2007-05-23 | [
[
"Brandt",
"Howard E.",
""
]
] | Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates of the observer. It is then useful to consider the tangent bundle of spacetime with spacetime in the base manifold and four-velocity space in the fiber. A physical basis for the differential geometric structure of the spacetime tangent bundle is provided by the universal upper limit on proper acceleration relative to the vacuum. It is then natural to consider a quantum field having a vanishing eigenvalue when acted on by the Laplace-Beltrami operator of the spacetime tangent bundle. On this basis a quantum field theory can be constructed having a built-in intrinsic regularization at the Planck scale, and finite vacuum energy density. |
2408.02747 | Ilija Buric | Ilija Buric, Francesco Russo, Volker Schomerus and Alessandro Vichi | Thermal One-point Functions and Their Partial Wave Decomposition | null | null | null | null | hep-th gr-qc math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this work we address partial wave decompositions of thermal one-point
functions in conformal field theories on $S^1 \times S^{d-1}$. With the help of
Casimir differential equations we develop efficient algorithms to compute the
relevant conformal blocks for an external field of arbitrary spin and with any
spin exchange along the thermal circle, at least in three dimensions. This is
achieved by identifying solutions to the Casimir equations with a special class
of spherical functions in the harmonic analysis of the conformal group. The
resulting blocks are then applied to study the decomposition of one-point
functions of the scalar $\phi^2$ and the stress tensor $T$ for a
three-dimensional free scalar field $\phi$. We are able to read off averaged
OPE coefficients into exchanged fields of high weight and spin for a complete
set of tensor structures. We also extract an asymptotic behaviour of conformal
blocks and use it to analyse the density of heavy-heavy-light OPE coefficients
for spinning operators, comparing it with semi-classical predictions, such as
the dimensions of operators at large charge.
| [
{
"created": "Mon, 5 Aug 2024 18:06:17 GMT",
"version": "v1"
}
] | 2024-08-07 | [
[
"Buric",
"Ilija",
""
],
[
"Russo",
"Francesco",
""
],
[
"Schomerus",
"Volker",
""
],
[
"Vichi",
"Alessandro",
""
]
] | In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on $S^1 \times S^{d-1}$. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant conformal blocks for an external field of arbitrary spin and with any spin exchange along the thermal circle, at least in three dimensions. This is achieved by identifying solutions to the Casimir equations with a special class of spherical functions in the harmonic analysis of the conformal group. The resulting blocks are then applied to study the decomposition of one-point functions of the scalar $\phi^2$ and the stress tensor $T$ for a three-dimensional free scalar field $\phi$. We are able to read off averaged OPE coefficients into exchanged fields of high weight and spin for a complete set of tensor structures. We also extract an asymptotic behaviour of conformal blocks and use it to analyse the density of heavy-heavy-light OPE coefficients for spinning operators, comparing it with semi-classical predictions, such as the dimensions of operators at large charge. |
1401.5106 | Takaaki Ishii | Takaaki Ishii, Shunichiro Kinoshita, Keiju Murata and Norihiro
Tanahashi | Dynamical Meson Melting in Holography | 42 pages, 23 figures, v2: references added | null | 10.1007/JHEP04(2014)099 | AP-GR-108, CCTP-2014-26, CCQCN-2014-17, IPMU14-0004, OCU-PHYS-396 | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We discuss mesons in thermalizing gluon backgrounds in the N=2 supersymmetric
QCD using the gravity dual. We numerically compute the dynamics of a probe
D7-brane in the Vaidya-AdS geometry that corresponds to a D3-brane background
thermalizing from zero to finite temperatures by energy injection. In static
backgrounds, it has been known that there are two kinds of brane embeddings
where the brane intersects the black hole or not. They correspond to the phases
with melted or stable mesons. In our dynamical setup, we obtain three cases
depending on final temperatures and injection time scales. The brane stays
outside of the black hole horizon when the final temperature is low, while it
intersects the horizon and settles down to the static equilibrium state when
the final temperature is high. Between these two cases, we find the overeager
case where the brane dynamically intersects the horizon although the final
temperature is not high enough for a static brane to intersect the horizon. The
interpretation of this phenomenon in the dual field theory is meson melting due
to non-thermal effects caused by rapid energy injection. In addition, we
comment on the late time evolution of the brane and a possibility of its
reconnection.
| [
{
"created": "Mon, 20 Jan 2014 22:00:50 GMT",
"version": "v1"
},
{
"created": "Tue, 28 Jan 2014 18:39:45 GMT",
"version": "v2"
}
] | 2015-06-18 | [
[
"Ishii",
"Takaaki",
""
],
[
"Kinoshita",
"Shunichiro",
""
],
[
"Murata",
"Keiju",
""
],
[
"Tanahashi",
"Norihiro",
""
]
] | We discuss mesons in thermalizing gluon backgrounds in the N=2 supersymmetric QCD using the gravity dual. We numerically compute the dynamics of a probe D7-brane in the Vaidya-AdS geometry that corresponds to a D3-brane background thermalizing from zero to finite temperatures by energy injection. In static backgrounds, it has been known that there are two kinds of brane embeddings where the brane intersects the black hole or not. They correspond to the phases with melted or stable mesons. In our dynamical setup, we obtain three cases depending on final temperatures and injection time scales. The brane stays outside of the black hole horizon when the final temperature is low, while it intersects the horizon and settles down to the static equilibrium state when the final temperature is high. Between these two cases, we find the overeager case where the brane dynamically intersects the horizon although the final temperature is not high enough for a static brane to intersect the horizon. The interpretation of this phenomenon in the dual field theory is meson melting due to non-thermal effects caused by rapid energy injection. In addition, we comment on the late time evolution of the brane and a possibility of its reconnection. |
2302.04736 | Nicolas Wink | Friederike Ihssen, Franz R. Sattler, Nicolas Wink | Numerical RG-time integration of the effective potential: Analysis and
Benchmark | 22 pages, 13 figures | null | 10.1103/PhysRevD.107.114009 | null | hep-th cond-mat.stat-mech physics.comp-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We investigate the RG-time integration of the effective potential in the
functional renormalization group in the presence of spontaneous symmetry
breaking and its subsequent convexity restoration on the example of a scalar
theory in $d=3$. The features of this setup are common to many physical models
and our results are, therefore, directly applicable to a variety of situations.
We provide exhaustive work-precision benchmarks and numerical stability
analyses by considering the combination of different discrete formulations of
the flow equation and a large collection of different algorithms. The results
are explained by using the different components entering the RG-time
integration process and the eigenvalue structure of the discrete system.
Particularly, the combination of Rosenbrock methods, implicit multistep methods
or certain (diagonally) implicit Runge-Kutta methods with exact or autodiff
Jacobians proves to be very potent. Furthermore, a reformulation in a
logarithmic variable circumvents issues related to the singularity bound in the
flat regime of the potential.
| [
{
"created": "Thu, 9 Feb 2023 16:16:05 GMT",
"version": "v1"
}
] | 2023-06-21 | [
[
"Ihssen",
"Friederike",
""
],
[
"Sattler",
"Franz R.",
""
],
[
"Wink",
"Nicolas",
""
]
] | We investigate the RG-time integration of the effective potential in the functional renormalization group in the presence of spontaneous symmetry breaking and its subsequent convexity restoration on the example of a scalar theory in $d=3$. The features of this setup are common to many physical models and our results are, therefore, directly applicable to a variety of situations. We provide exhaustive work-precision benchmarks and numerical stability analyses by considering the combination of different discrete formulations of the flow equation and a large collection of different algorithms. The results are explained by using the different components entering the RG-time integration process and the eigenvalue structure of the discrete system. Particularly, the combination of Rosenbrock methods, implicit multistep methods or certain (diagonally) implicit Runge-Kutta methods with exact or autodiff Jacobians proves to be very potent. Furthermore, a reformulation in a logarithmic variable circumvents issues related to the singularity bound in the flat regime of the potential. |
0710.1129 | Leonard Susskind | Leonard Susskind | The Census Taker's Hat | 69 pages, 15 figures | null | null | null | hep-th | null | If the observable universe really is a hologram, then of what sort? Is it
rich enough to keep track of an eternally inflating multiverse? What physical
and mathematical principles underlie it? Is the hologram a lower dimensional
quantum field theory, and if so, how many dimensions are explicit, and how many
"emerge?" Does the Holographic description provide clues for defining a
probability measure on the Landscape?
The purpose of this lecture is first, to briefly review a proposal for a
holographic cosmology by Freivogel, Sekino, Susskind, and Yeh (FSSY), and then
to develop a physical interpretation in terms of a "Cosmic Census Taker:" an
idea introduced in reference [1]. The mathematical structure--a hybrid of the
Wheeler DeWitt formalism and holography--is a boundary "Liouville" field
theory, whose UV/IR duality is closely related to the time evolution of the
Census Taker's observations. That time evolution is represented by the
renormalization-group flow of the Liouville theory.
Although quite general, the Census Taker idea was originally introduced in
\cite{shenker}, for the purpose of counting bubbles that collide with the
Census Taker's bubble. The "Persistence of Memory" phenomenon discovered by
Garriga, Guth, and Vilenkin, has a natural RG interpretation, as does slow roll
inflation. The RG flow and the related C-theorem are closely connected with
generalized entropy bounds.
| [
{
"created": "Fri, 5 Oct 2007 03:33:25 GMT",
"version": "v1"
}
] | 2007-10-08 | [
[
"Susskind",
"Leonard",
""
]
] | If the observable universe really is a hologram, then of what sort? Is it rich enough to keep track of an eternally inflating multiverse? What physical and mathematical principles underlie it? Is the hologram a lower dimensional quantum field theory, and if so, how many dimensions are explicit, and how many "emerge?" Does the Holographic description provide clues for defining a probability measure on the Landscape? The purpose of this lecture is first, to briefly review a proposal for a holographic cosmology by Freivogel, Sekino, Susskind, and Yeh (FSSY), and then to develop a physical interpretation in terms of a "Cosmic Census Taker:" an idea introduced in reference [1]. The mathematical structure--a hybrid of the Wheeler DeWitt formalism and holography--is a boundary "Liouville" field theory, whose UV/IR duality is closely related to the time evolution of the Census Taker's observations. That time evolution is represented by the renormalization-group flow of the Liouville theory. Although quite general, the Census Taker idea was originally introduced in \cite{shenker}, for the purpose of counting bubbles that collide with the Census Taker's bubble. The "Persistence of Memory" phenomenon discovered by Garriga, Guth, and Vilenkin, has a natural RG interpretation, as does slow roll inflation. The RG flow and the related C-theorem are closely connected with generalized entropy bounds. |
2210.04575 | Abouzeid Shalaby Prof. | Abouzeid M. Shalaby | High-Order Parametrization of the Hypergeometric-Meijer Approximants | This is a self-contained version of the Hypergeometric-Meijer
approximation algorithm we introduced before. In this version, one can
parameterize high orders in short time and can accommodate non-perturbative
parameters as well | null | 10.1016/j.aop.2023.169376 | null | hep-th | http://creativecommons.org/licenses/by/4.0/ | In previous articles, we showed that, based on large-order asymptotic
behavior, one can approximate a divergent series via the parametrization of a
specific hypergeometric approximant. The analytical continuation is then
carried out through a Mellin-Barnes integral representation of the
hypergeometric approximant or equivalently using an equivalent form of the
Meijer G-Function. The parametrization process involves the solution of a
non-linear set of coupled equations which is hard to achieve (might be
impossible) for high orders using normal PCs. In this work, we extend the
approximation algorithm to accommodate any order (high or low) of the given
series in a short time. The extension also allows us to employ non-perturbative
information like strong-coupling and large-order asymptotic data which are
always used to accelerate the convergence. We applied the algorithm for
different orders (up to O($29$)) of the ground state energy of the $x^4$
anharmonic oscillator with and without the non-perturbative information. We
also considered the available $20$ orders for the ground sate energy of the
$\mathcal{PT}-$symmetric $ix^{3}$ anharmonic oscillator as well as the given
$20$ orders of its strong-coupling expansion or equivalently the Yang-Lee
model. For high order weak-coupling parametrization, accurate results have been
obtained for the ground state energy and the non-perturbative parameters
describing strong-coupling and large-order asymptotic behaviors. The employment
of the non-perturbative data accelerated the convergence very clearly. The High
temperature expansion for the susceptibility within the $SQ$ lattice has been
also considered and led to accurate prediction for the critical exponent and
critical temperature.
| [
{
"created": "Mon, 10 Oct 2022 11:30:43 GMT",
"version": "v1"
}
] | 2023-08-09 | [
[
"Shalaby",
"Abouzeid M.",
""
]
] | In previous articles, we showed that, based on large-order asymptotic behavior, one can approximate a divergent series via the parametrization of a specific hypergeometric approximant. The analytical continuation is then carried out through a Mellin-Barnes integral representation of the hypergeometric approximant or equivalently using an equivalent form of the Meijer G-Function. The parametrization process involves the solution of a non-linear set of coupled equations which is hard to achieve (might be impossible) for high orders using normal PCs. In this work, we extend the approximation algorithm to accommodate any order (high or low) of the given series in a short time. The extension also allows us to employ non-perturbative information like strong-coupling and large-order asymptotic data which are always used to accelerate the convergence. We applied the algorithm for different orders (up to O($29$)) of the ground state energy of the $x^4$ anharmonic oscillator with and without the non-perturbative information. We also considered the available $20$ orders for the ground sate energy of the $\mathcal{PT}-$symmetric $ix^{3}$ anharmonic oscillator as well as the given $20$ orders of its strong-coupling expansion or equivalently the Yang-Lee model. For high order weak-coupling parametrization, accurate results have been obtained for the ground state energy and the non-perturbative parameters describing strong-coupling and large-order asymptotic behaviors. The employment of the non-perturbative data accelerated the convergence very clearly. The High temperature expansion for the susceptibility within the $SQ$ lattice has been also considered and led to accurate prediction for the critical exponent and critical temperature. |
hep-th/0607155 | Ashoke Sen | Justin R. David, Dileep P. Jatkar, Ashoke Sen | Dyon Spectrum in N=4 Supersymmetric Type II String Theories | LaTeX file, 32 pages; v2:minor changes | JHEP 0611:073,2006 | 10.1088/1126-6708/2006/11/073 | null | hep-th | null | We compute the spectrum of quarter BPS dyons in freely acting Z_2 and Z_3
orbifolds of type II string theory compactified on a six dimensional torus. For
large charges the result for statistical entropy computed from the degeneracy
formula agrees with the corresponding black hole entropy to first non-leading
order after taking into account corrections due to the curvature squared terms
in the effective action. The result is significant since in these theories the
entropy of a small black hole, computed using the curvature squared corrections
to the effective action, fails to reproduce the statistical entropy associated
with elementary string states.
| [
{
"created": "Fri, 21 Jul 2006 05:37:24 GMT",
"version": "v1"
},
{
"created": "Wed, 13 Sep 2006 02:17:40 GMT",
"version": "v2"
}
] | 2009-11-11 | [
[
"David",
"Justin R.",
""
],
[
"Jatkar",
"Dileep P.",
""
],
[
"Sen",
"Ashoke",
""
]
] | We compute the spectrum of quarter BPS dyons in freely acting Z_2 and Z_3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula agrees with the corresponding black hole entropy to first non-leading order after taking into account corrections due to the curvature squared terms in the effective action. The result is significant since in these theories the entropy of a small black hole, computed using the curvature squared corrections to the effective action, fails to reproduce the statistical entropy associated with elementary string states. |
hep-th/0302101 | Sultan Catto | Sultan Catto | Effective Hadronic Lagrangians Based on QCD: Potential Models and
Skyrmions | 81 pages, Latex format | null | null | null | hep-th | null | An approximate hadronic symmetry based on spin and flavor independence and
broken by spin and mass dependent terms is shown to follow from QCD. This
symmetry justifies the SU(6) classification scheme, but is more general in
allowing its supersymmetric extension based on a diquark-antiquark symmetry. It
will be shown that the same supersymmetry is also implied in the skyrmion type
effective Lagrangian which could be extracted from QCD. Predictions of the
Skyrme model is improved by using different realizations of the chiral group.
| [
{
"created": "Thu, 13 Feb 2003 18:09:36 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Catto",
"Sultan",
""
]
] | An approximate hadronic symmetry based on spin and flavor independence and broken by spin and mass dependent terms is shown to follow from QCD. This symmetry justifies the SU(6) classification scheme, but is more general in allowing its supersymmetric extension based on a diquark-antiquark symmetry. It will be shown that the same supersymmetry is also implied in the skyrmion type effective Lagrangian which could be extracted from QCD. Predictions of the Skyrme model is improved by using different realizations of the chiral group. |
hep-th/0604190 | Nissan Itzhaki | Nissan Itzhaki | A Comment on Technical Naturalness and the Cosmological Constant | 10 pages, ref. added | JHEP 0608 (2006) 020 | 10.1088/1126-6708/2006/08/020 | null | hep-th hep-ph | null | We propose a model of dynamical relaxation of the cosmological constant.
Technical naturalness of the model and the present value of the vacuum energy
density imply an upper bound on the supersymmetry breaking scale and the
reheating temperature at the TeV scale.
| [
{
"created": "Tue, 25 Apr 2006 18:58:05 GMT",
"version": "v1"
},
{
"created": "Tue, 25 Apr 2006 20:00:17 GMT",
"version": "v2"
},
{
"created": "Tue, 2 May 2006 13:38:12 GMT",
"version": "v3"
},
{
"created": "Fri, 4 Aug 2006 13:26:05 GMT",
"version": "v4"
},
{
"created": "Tue, 26 Sep 2006 13:31:26 GMT",
"version": "v5"
}
] | 2009-11-11 | [
[
"Itzhaki",
"Nissan",
""
]
] | We propose a model of dynamical relaxation of the cosmological constant. Technical naturalness of the model and the present value of the vacuum energy density imply an upper bound on the supersymmetry breaking scale and the reheating temperature at the TeV scale. |
0910.4134 | Jacobus Verbaarschot | J.J.M. Verbaarschot | Handbook Article on Applications of Random Matrix Theory to QCD | 31 pages, 5 figures. Invited article for the Oxford Handbook of
Random Matrix Theory | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this chapter of the Oxford Handbook of Random Matrix Theory we introduce
chiral Random Matrix Theories with the global symmetries of QCD. In the
microscopic domain, these theories reproduce the mass and chemical potential
dependence of QCD. The main focus of this chapter is on the spectral properties
of the QCD Dirac operator and relations between chiral Random Matrix Theories
and chiral Lagrangians. Both spectra of the anti-hermitian Dirac operator and
spectra of the nonhermitian Dirac operator at nonzero chemical potential are
discussed.
| [
{
"created": "Wed, 21 Oct 2009 19:20:02 GMT",
"version": "v1"
}
] | 2009-10-22 | [
[
"Verbaarschot",
"J. J. M.",
""
]
] | In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of QCD. The main focus of this chapter is on the spectral properties of the QCD Dirac operator and relations between chiral Random Matrix Theories and chiral Lagrangians. Both spectra of the anti-hermitian Dirac operator and spectra of the nonhermitian Dirac operator at nonzero chemical potential are discussed. |
hep-th/9512009 | Tetsuyuki Ochiai | Tetsuyuki Ochiai | Neutral Multi-Instanton as a Bridge from Weak to Strong Coupling phase
in Two Dimensional QCD | 26pages, Latex, 7 Postscript figures included by epsf | null | null | EPHOU-95-005 | hep-th | null | Using a contour integral representation we analyze the multi-instanton sector
in two dimensional $U(N)$ Yang-Mills theory on a sphere and argue the role of
multi-instanton in the large $N$ phase transition. In the strong coupling
region at the large $N$ , we encounter ``singular saddle point''. Because of
this situation, ``neutral'' configurations of the multi-instanton are dominant
in this region. Based on the ``neutral'' multi-instanton approximation we
numerically calculate the multi-instanton amplitude , the free energies and the
Wilson loops for finite $N$ . We also compare our results with the large $N$
exact solution of the free energy and the Wilson loop and argue some problems.
We find the ``neutral'' multi-instanton contribution bridges the gap between
weak and strong coupling phase.
| [
{
"created": "Mon, 4 Dec 1995 07:28:46 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Ochiai",
"Tetsuyuki",
""
]
] | Using a contour integral representation we analyze the multi-instanton sector in two dimensional $U(N)$ Yang-Mills theory on a sphere and argue the role of multi-instanton in the large $N$ phase transition. In the strong coupling region at the large $N$ , we encounter ``singular saddle point''. Because of this situation, ``neutral'' configurations of the multi-instanton are dominant in this region. Based on the ``neutral'' multi-instanton approximation we numerically calculate the multi-instanton amplitude , the free energies and the Wilson loops for finite $N$ . We also compare our results with the large $N$ exact solution of the free energy and the Wilson loop and argue some problems. We find the ``neutral'' multi-instanton contribution bridges the gap between weak and strong coupling phase. |
1512.06651 | Bayram Tekin | Emel Altas, Bayram Tekin | Holographically Viable Extensions of Topologically Massive and Minimal
Massive Gravity? | 10 pages, references added, almost matches the published version | Phys. Rev. D 93, 025033 (2016) | 10.1103/PhysRevD.93.025033 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Recently, an extension of the topologically massive gravity (TMG) in $2+1$
dimensions, dubbed as minimal massive gravity (MMG), was found which is free of
the bulk-boundary unitarity clash that inflicts the former theory and all the
other known three dimensional theories. Field equations of MMG differ from
those of TMG at quadratic terms in the curvature that do not come from the
variation of an action depending on the metric alone. Here we show that MMG is
a unique theory and there does not exist a deformation of TMG or MMG at the
cubic and quartic order (and beyond) in the curvature that is consistent at the
level of the field equations. The only extension of TMG with the desired bulk
and boundary properties having a single massive degree of freedom is MMG.
| [
{
"created": "Mon, 21 Dec 2015 14:52:04 GMT",
"version": "v1"
},
{
"created": "Wed, 23 Dec 2015 11:23:11 GMT",
"version": "v2"
},
{
"created": "Fri, 26 Feb 2016 10:50:53 GMT",
"version": "v3"
}
] | 2016-02-29 | [
[
"Altas",
"Emel",
""
],
[
"Tekin",
"Bayram",
""
]
] | Recently, an extension of the topologically massive gravity (TMG) in $2+1$ dimensions, dubbed as minimal massive gravity (MMG), was found which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three dimensional theories. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is consistent at the level of the field equations. The only extension of TMG with the desired bulk and boundary properties having a single massive degree of freedom is MMG. |
1306.5644 | Alexander Manashov | V.M. Braun, A.N. Manashov | Evolution equations beyond one loop from conformal symmetry | 19 pages, 3 figures | Eur.Phys.J. C73 (2013) 2544 | 10.1140/epjc/s10052-013-2544-1 | null | hep-th hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study implications of exact conformal invariance of scalar quantum field
theories at the critical point in non-integer dimensions for the evolution
kernels of the light-ray operators in physical (integer) dimensions. We
demonstrate that all constraints due the conformal symmetry are encoded in the
form of the generators of the collinear sl(2) subgroup. Two of them, S_- and
S_0, can be fixed at all loops in terms of the evolution kernel, while the
generator of special conformal transformations, S_+, receives nontrivial
corrections which can be calculated order by order in perturbation theory.
Provided that the generator S_+ is known at the k-1 loop order, one can fix the
evolution kernel in physical dimension to the k-loop accuracy up to terms that
are invariant with respect to the tree-level generators. The invariant parts
can easily be restored from the anomalous dimensions. The method is illustrated
on two examples: The O(n)-symmetric phi^4 theory in d=4 to the three-loop
accuracy, and the su(n) matrix phi^3 theory in d=6 to the two-loop accuracy. We
expect that the same technique can be used in gauge theories e.g. in QCD.
| [
{
"created": "Mon, 24 Jun 2013 14:42:07 GMT",
"version": "v1"
}
] | 2014-10-20 | [
[
"Braun",
"V. M.",
""
],
[
"Manashov",
"A. N.",
""
]
] | We study implications of exact conformal invariance of scalar quantum field theories at the critical point in non-integer dimensions for the evolution kernels of the light-ray operators in physical (integer) dimensions. We demonstrate that all constraints due the conformal symmetry are encoded in the form of the generators of the collinear sl(2) subgroup. Two of them, S_- and S_0, can be fixed at all loops in terms of the evolution kernel, while the generator of special conformal transformations, S_+, receives nontrivial corrections which can be calculated order by order in perturbation theory. Provided that the generator S_+ is known at the k-1 loop order, one can fix the evolution kernel in physical dimension to the k-loop accuracy up to terms that are invariant with respect to the tree-level generators. The invariant parts can easily be restored from the anomalous dimensions. The method is illustrated on two examples: The O(n)-symmetric phi^4 theory in d=4 to the three-loop accuracy, and the su(n) matrix phi^3 theory in d=6 to the two-loop accuracy. We expect that the same technique can be used in gauge theories e.g. in QCD. |
1004.4483 | Ljubica Davidovic | Lj. Davidovi\'c and B. Sazdovi\'c | Noncommutativity in weakly curved background by canonical methods | 27 pages | Phys.Rev.D83:066014,2011 | 10.1103/PhysRevD.83.066014 | null | hep-th math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Using canonical method we investigate $Dp-$brane world-volume
noncommutativity in weakly curved background. The term weakly curved means that
in the leading order, the source of non-flatness is infinitesimally small
Kalb-Ramond field $B_{\mu\nu}$ linear in coordinate, while the Ricci tensor
does not contribute being the infinitesimal of the second order. On the
solution of boundary conditions, we find simple expression for the space-time
coordinates in terms of the effective coordinates and momenta. This basic
relation helped us to prove that noncommutativity appears only on the
world-sheet boundary. The noncommutativity parameter has a standard form but
with infinitesimally small and coordinate dependent antisymmetric tensor
$B_{\mu\nu}$. This result coincides with that obtained on the group manifolds
in the limit of the large level $n$ of current algebra. After quantization the
algebra of functions on Dp-brane world-volume is represented with the
Kontsevich star product instead of the Moyal one in the flat background.
| [
{
"created": "Mon, 26 Apr 2010 11:12:09 GMT",
"version": "v1"
},
{
"created": "Tue, 15 Nov 2011 14:48:57 GMT",
"version": "v2"
}
] | 2011-11-16 | [
[
"Davidović",
"Lj.",
""
],
[
"Sazdović",
"B.",
""
]
] | Using canonical method we investigate $Dp-$brane world-volume noncommutativity in weakly curved background. The term weakly curved means that in the leading order, the source of non-flatness is infinitesimally small Kalb-Ramond field $B_{\mu\nu}$ linear in coordinate, while the Ricci tensor does not contribute being the infinitesimal of the second order. On the solution of boundary conditions, we find simple expression for the space-time coordinates in terms of the effective coordinates and momenta. This basic relation helped us to prove that noncommutativity appears only on the world-sheet boundary. The noncommutativity parameter has a standard form but with infinitesimally small and coordinate dependent antisymmetric tensor $B_{\mu\nu}$. This result coincides with that obtained on the group manifolds in the limit of the large level $n$ of current algebra. After quantization the algebra of functions on Dp-brane world-volume is represented with the Kontsevich star product instead of the Moyal one in the flat background. |
0903.5502 | Shinichiro Yamato | Shinichiro Yamato | The Laue pattern and the Rydberg formula in classical soliton models | 5 pages, 4 figures | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In recent researches of the dynamics of solitons, it is gradually revealed
that oscillation modes play a crucial role when we analyze the dynamics of
solitons. Some dynamical properties of solitons on external potentials are
studied with both numerical methods and analytical methods. In this paper, we
propose a method to deal with such oscillation modes of solitons in potential
wells. We show that oscillations of a soliton is described by the Klein-Gordon
equation with an external potential. Although this analysis does not seems to
give quantitative scattering amplitude of a soliton itself, it explains
qualitative pictures of scattering. As a result of our analysis, when a soliton
is scattered in a cyclic potential, the Laue pattern emerges. Furthermore,
since our analysis is based on the Klein-Gordon equation, a discrete frequency
spectrum of a soliton is obtained when it is bounded by some potentials. What
is especially important is that this analysis predicts a frequency spectrum of
a soliton in the Coulomb potential and then we find that this system absorbs
external waves with specific frequencies described by the Rydberg formula.
| [
{
"created": "Tue, 31 Mar 2009 15:36:45 GMT",
"version": "v1"
}
] | 2009-04-01 | [
[
"Yamato",
"Shinichiro",
""
]
] | In recent researches of the dynamics of solitons, it is gradually revealed that oscillation modes play a crucial role when we analyze the dynamics of solitons. Some dynamical properties of solitons on external potentials are studied with both numerical methods and analytical methods. In this paper, we propose a method to deal with such oscillation modes of solitons in potential wells. We show that oscillations of a soliton is described by the Klein-Gordon equation with an external potential. Although this analysis does not seems to give quantitative scattering amplitude of a soliton itself, it explains qualitative pictures of scattering. As a result of our analysis, when a soliton is scattered in a cyclic potential, the Laue pattern emerges. Furthermore, since our analysis is based on the Klein-Gordon equation, a discrete frequency spectrum of a soliton is obtained when it is bounded by some potentials. What is especially important is that this analysis predicts a frequency spectrum of a soliton in the Coulomb potential and then we find that this system absorbs external waves with specific frequencies described by the Rydberg formula. |
0806.0455 | Soumitra SenGupta | Ratna Koley, Joydip Mitra, Soumitra SenGupta | Fermion localization in generalised Randall Sundrum model | 5 pages, 7 figures, Revtex | Phys.Rev.D79:041902,2009 | 10.1103/PhysRevD.79.041902 | null | hep-th gr-qc hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A generalized two-brane Randall-Sundrum warped braneworld model admits of
solutions of the warp factor for both positive or negative cosmological
constant on the visible 3-brane which can resolve the naturalness problem in
connection with the fine tuning of Higgs mass in the standard model of
elementary particles. To explore the location of the standard model fermions in
such a generalized warped model, we, in this work, determine the dependence of
the localization profile of a bulk fermion on the brane cosmological constant
brane tension and the bulk fermion mass. Our results reveal that for a positive
and small value of the induced cosmological constant a bulk fermion is
localized close to the brane. On the other hand for a visible brane with
negative cosmological constant and positive tension, the fermions are localized
inside the bulk leading to phenomenologically interesting possibilities.
| [
{
"created": "Tue, 3 Jun 2008 07:40:02 GMT",
"version": "v1"
},
{
"created": "Tue, 27 Jan 2009 10:05:40 GMT",
"version": "v2"
}
] | 2010-05-12 | [
[
"Koley",
"Ratna",
""
],
[
"Mitra",
"Joydip",
""
],
[
"SenGupta",
"Soumitra",
""
]
] | A generalized two-brane Randall-Sundrum warped braneworld model admits of solutions of the warp factor for both positive or negative cosmological constant on the visible 3-brane which can resolve the naturalness problem in connection with the fine tuning of Higgs mass in the standard model of elementary particles. To explore the location of the standard model fermions in such a generalized warped model, we, in this work, determine the dependence of the localization profile of a bulk fermion on the brane cosmological constant brane tension and the bulk fermion mass. Our results reveal that for a positive and small value of the induced cosmological constant a bulk fermion is localized close to the brane. On the other hand for a visible brane with negative cosmological constant and positive tension, the fermions are localized inside the bulk leading to phenomenologically interesting possibilities. |
hep-th/0105071 | Svozil Karl | Volkmar Putz and Karl Svozil | Quantum electrodynamics in the squeezed vacuum state: Electron mass
shift | 6 pages, minor corrections | Nuovo Cim. B119 (2004) 175-179 | 10.1393/ncb/i2004-10051-8 | null | hep-th | null | Due to the nonvanishing average photon population of the squeezed vacuum
state, finite corrections to the scattering matrix are obtained. The lowest
order contribution to the electron mass shift for a one mode squeezed vacuum
state is given by $\delta m(\Omega, s)/m=\alpha (2/\pi)(\Omega
/m)^2\sinh^2(s)$, where $\Omega$ and $s$ stand for the mode frequency and the
squeeze parameter and $\alpha$ for the fine structure constant, respectively.
| [
{
"created": "Tue, 8 May 2001 11:20:26 GMT",
"version": "v1"
},
{
"created": "Wed, 11 Dec 2002 14:40:55 GMT",
"version": "v2"
}
] | 2016-09-06 | [
[
"Putz",
"Volkmar",
""
],
[
"Svozil",
"Karl",
""
]
] | Due to the nonvanishing average photon population of the squeezed vacuum state, finite corrections to the scattering matrix are obtained. The lowest order contribution to the electron mass shift for a one mode squeezed vacuum state is given by $\delta m(\Omega, s)/m=\alpha (2/\pi)(\Omega /m)^2\sinh^2(s)$, where $\Omega$ and $s$ stand for the mode frequency and the squeeze parameter and $\alpha$ for the fine structure constant, respectively. |
2207.11262 | Hengameh Bagherian | Hengameh Bagherian, Matthew Reece, and Weishuang Linda Xu | The Inflated Chern-Simons Number in Spectator Chromo-Natural Inflation | 33 pages, 3 figures | null | 10.1007/JHEP01(2023)099 | null | hep-th astro-ph.CO hep-ph | http://creativecommons.org/licenses/by/4.0/ | The chromo-natural inflation (CNI) scenario predicts a potentially detectable
chiral gravitational wave signal, generated by a Chern-Simons coupling between
a rolling scalar axion field and an SU(2) gauge field with an
isotropy-preserving classical background during inflation. However, the
generation of this signal requires a very large integer Chern-Simons level,
which can be challenging to explain or embed in a UV-complete model. We show
that this challenge persists in the phenomenologically viable spectator field
CNI (S-CNI) model. Furthermore, we show that a clockwork scenario giving rise
to a large integer as a product of small integers can never produce a
Chern-Simons level large enough to have successful S-CNI phenomenology. We
briefly discuss other constraints on the model, both in effective field theory
based on partial-wave unitarity bounds and in quantum gravity based on the Weak
Gravity Conjecture, which may be relevant for further explorations of
alternative UV completions.
| [
{
"created": "Fri, 22 Jul 2022 18:00:00 GMT",
"version": "v1"
}
] | 2023-01-31 | [
[
"Bagherian",
"Hengameh",
""
],
[
"Reece",
"Matthew",
""
],
[
"Xu",
"Weishuang Linda",
""
]
] | The chromo-natural inflation (CNI) scenario predicts a potentially detectable chiral gravitational wave signal, generated by a Chern-Simons coupling between a rolling scalar axion field and an SU(2) gauge field with an isotropy-preserving classical background during inflation. However, the generation of this signal requires a very large integer Chern-Simons level, which can be challenging to explain or embed in a UV-complete model. We show that this challenge persists in the phenomenologically viable spectator field CNI (S-CNI) model. Furthermore, we show that a clockwork scenario giving rise to a large integer as a product of small integers can never produce a Chern-Simons level large enough to have successful S-CNI phenomenology. We briefly discuss other constraints on the model, both in effective field theory based on partial-wave unitarity bounds and in quantum gravity based on the Weak Gravity Conjecture, which may be relevant for further explorations of alternative UV completions. |
1903.11806 | Kengo Maeda | Akihiro Ishibashi, Kengo Maeda, and Eric Mefford | Achronal ANEC, Weak Cosmic Censorship, and AdS/CFT duality | 10 pages, 3 figures | Phys. Rev. D 100, 066008 (2019) | 10.1103/PhysRevD.100.066008 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We examine the achronal averaged null energy condition~(ANEC) for a class of
conformal field theories~(CFT) at strong coupling in curved spacetime. By
applying the AdS/CFT duality, we find holographic models which violate the
achronal ANEC for $3+1$ and $4+1$-dimensional boundary theories. In our model,
the bulk spacetime is an asymptotically AdS vacuum bubble solution with neither
causality violation nor singularities. The conformal boundary of our bubble
solution is asymptotically flat and is causally proper in the sense that a
"fastest null geodesics" connecting any two points on the boundary must lie
entirely on the boundary. We show that conversely, if the spacetime fails to
have this causally proper nature, then there must be a naked singularity in the
bulk.
| [
{
"created": "Thu, 28 Mar 2019 06:59:03 GMT",
"version": "v1"
}
] | 2019-09-11 | [
[
"Ishibashi",
"Akihiro",
""
],
[
"Maeda",
"Kengo",
""
],
[
"Mefford",
"Eric",
""
]
] | We examine the achronal averaged null energy condition~(ANEC) for a class of conformal field theories~(CFT) at strong coupling in curved spacetime. By applying the AdS/CFT duality, we find holographic models which violate the achronal ANEC for $3+1$ and $4+1$-dimensional boundary theories. In our model, the bulk spacetime is an asymptotically AdS vacuum bubble solution with neither causality violation nor singularities. The conformal boundary of our bubble solution is asymptotically flat and is causally proper in the sense that a "fastest null geodesics" connecting any two points on the boundary must lie entirely on the boundary. We show that conversely, if the spacetime fails to have this causally proper nature, then there must be a naked singularity in the bulk. |
2205.05705 | Andrew Svesko | Juan F. Pedraza, Andrea Russo, Andrew Svesko and Zachary Weller-Davies | Computing spacetime | 9 pages, 2 figures, Received honorable mention for the 2022 Essay
Competition of the Gravity Research Foundation; References added, to appear
in the October 2022 Special Issue of the International Journal of Modern
Physics D | Int.J.Mod.Phys.D 31 (2022) 14, 2242010 | 10.1142/S021827182242010X | IFT-UAM/CSIC-22-54 | hep-th gr-qc quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Inspired by the universality of computation, we advocate for a principle of
spacetime complexity, where gravity arises as a consequence of spacetime
optimizing the computational cost of its own quantum dynamics. This principle
is explicitly realized in the context of the Anti-de Sitter/Conformal Field
Theory correspondence, where complexity is naturally understood in terms of
state preparation via Euclidean path integrals, and Einstein's equations emerge
from the laws of quantum complexity. We visualize spacetime complexity using
Lorentzian threads which, conceptually, represent the operations needed to
prepare a quantum state in a tensor network discretizing spacetime. Thus,
spacetime itself evolves via optimized computation.
| [
{
"created": "Wed, 11 May 2022 18:00:10 GMT",
"version": "v1"
},
{
"created": "Thu, 18 Aug 2022 09:21:54 GMT",
"version": "v2"
}
] | 2022-12-14 | [
[
"Pedraza",
"Juan F.",
""
],
[
"Russo",
"Andrea",
""
],
[
"Svesko",
"Andrew",
""
],
[
"Weller-Davies",
"Zachary",
""
]
] | Inspired by the universality of computation, we advocate for a principle of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its own quantum dynamics. This principle is explicitly realized in the context of the Anti-de Sitter/Conformal Field Theory correspondence, where complexity is naturally understood in terms of state preparation via Euclidean path integrals, and Einstein's equations emerge from the laws of quantum complexity. We visualize spacetime complexity using Lorentzian threads which, conceptually, represent the operations needed to prepare a quantum state in a tensor network discretizing spacetime. Thus, spacetime itself evolves via optimized computation. |
1903.02323 | Shamit Kachru | Murat Gunaydin, Shamit Kachru, Arnav Tripathy | Black holes and Bhargava's invariant theory | 22 pages; v2: minor changes, references added, reminiscences about
Peter Freund added by first author; v3: two footnotes, one note and
references added. Typos corrected | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Attractor black holes in type II string compactifications on $K3 \times T^2$
are in correspondence with equivalence classes of binary quadratic forms. The
discriminant of the quadratic form governs the black hole entropy, and the
count of attractor black holes at a given entropy is given by a class number.
Here, we show this tantalizing relationship between attractors and arithmetic
can be generalized to a rich family, connecting black holes in supergravity and
string models with analogous equivalence classes of more general forms under
the action of arithmetic groups. Many of the physical theories involved have
played an earlier role in the study of "magical" supergravities, while their
mathematical counterparts are directly related to geometry-of-numbers examples
in the work of Bhargava et. al.
This paper is dedicated to the memory of Peter Freund. The last section is
devoted to some of M.G's personal reminiscences of Peter Freund.
| [
{
"created": "Wed, 6 Mar 2019 11:24:20 GMT",
"version": "v1"
},
{
"created": "Thu, 10 Sep 2020 04:06:13 GMT",
"version": "v2"
},
{
"created": "Wed, 28 Oct 2020 02:31:04 GMT",
"version": "v3"
}
] | 2020-10-29 | [
[
"Gunaydin",
"Murat",
""
],
[
"Kachru",
"Shamit",
""
],
[
"Tripathy",
"Arnav",
""
]
] | Attractor black holes in type II string compactifications on $K3 \times T^2$ are in correspondence with equivalence classes of binary quadratic forms. The discriminant of the quadratic form governs the black hole entropy, and the count of attractor black holes at a given entropy is given by a class number. Here, we show this tantalizing relationship between attractors and arithmetic can be generalized to a rich family, connecting black holes in supergravity and string models with analogous equivalence classes of more general forms under the action of arithmetic groups. Many of the physical theories involved have played an earlier role in the study of "magical" supergravities, while their mathematical counterparts are directly related to geometry-of-numbers examples in the work of Bhargava et. al. This paper is dedicated to the memory of Peter Freund. The last section is devoted to some of M.G's personal reminiscences of Peter Freund. |
1211.7070 | Steven B. Giddings | Steven B. Giddings | Nonviolent nonlocality | 15 pages of text w/ 3 figures. v2: improved references, short comment
re parametric dependence v3: minor changes/corrections, matching version to
appear in PRD | null | 10.1103/PhysRevD.88.064023 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | If quantum mechanics governs nature, black holes must evolve unitarily,
providing a powerful constraint on the dynamics of quantum gravity. Such
evolution apparently must in particular be nonlocal, when described from the
usual semiclassical geometric picture, in order to transfer quantum information
into the outgoing state. While such transfer from a disintegrating black hole
has the dangerous potential to be violent to generic infalling observers, this
paper proposes the existence of a more innocuous form of information transfer,
to relatively soft modes in the black hole atmosphere. Simplified models for
such nonlocal transfer are described and parameterized, within a possibly more
basic framework of a Hilbert tensor network. Sufficiently sensitive
measurements by infalling observers may detect departures from Hawking's
predictions, and in generic models black holes decay more rapidly. Constraints
of consistency -- internally and with known and expected features of physics --
restrict the form of information transfer, and should provide important guides
to discovery of the principles and mechanisms of the more fundamental nonlocal
mechanics.
| [
{
"created": "Thu, 29 Nov 2012 21:00:07 GMT",
"version": "v1"
},
{
"created": "Thu, 3 Jan 2013 22:47:39 GMT",
"version": "v2"
},
{
"created": "Mon, 9 Sep 2013 22:05:39 GMT",
"version": "v3"
}
] | 2013-09-18 | [
[
"Giddings",
"Steven B.",
""
]
] | If quantum mechanics governs nature, black holes must evolve unitarily, providing a powerful constraint on the dynamics of quantum gravity. Such evolution apparently must in particular be nonlocal, when described from the usual semiclassical geometric picture, in order to transfer quantum information into the outgoing state. While such transfer from a disintegrating black hole has the dangerous potential to be violent to generic infalling observers, this paper proposes the existence of a more innocuous form of information transfer, to relatively soft modes in the black hole atmosphere. Simplified models for such nonlocal transfer are described and parameterized, within a possibly more basic framework of a Hilbert tensor network. Sufficiently sensitive measurements by infalling observers may detect departures from Hawking's predictions, and in generic models black holes decay more rapidly. Constraints of consistency -- internally and with known and expected features of physics -- restrict the form of information transfer, and should provide important guides to discovery of the principles and mechanisms of the more fundamental nonlocal mechanics. |
2203.16824 | Josef Kluson | J. Kluson | Note About D-Branes in Carrollian Background | 19 pages | null | null | null | hep-th | http://creativecommons.org/publicdomain/zero/1.0/ | This paper is devoted to the construction of stable and unstable Dp-branes in
generalized Carroll space-times. We also study tachyon solutions on the
world-volume of unstable Dp-brane in Carrollian background and discuss their
physical interpretations.
| [
{
"created": "Thu, 31 Mar 2022 06:15:34 GMT",
"version": "v1"
}
] | 2022-04-01 | [
[
"Kluson",
"J.",
""
]
] | This paper is devoted to the construction of stable and unstable Dp-branes in generalized Carroll space-times. We also study tachyon solutions on the world-volume of unstable Dp-brane in Carrollian background and discuss their physical interpretations. |
1209.2751 | Romulo Rougemont | M. S. Guimaraes, R. Rougemont, C. Wotzasek, C. A. D. Zarro | Julia-Toulouse approach to (d+1)-dimensional bosonized Schwinger model
with an application to large N QCD | Improved discussions, references added, 7 pages | Phys. Rev. D 86, 125039 (2012) | 10.1103/PhysRevD.86.125039 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The Julia-Toulouse approach for condensation of charges and defects is used
to show that the bosonized Schwinger model can be obtained through a
condensation of electric charges in 1+1 dimensions. The massive model is
derived by taking into account the presence of vortices over the electric
condensate, while the massless model is obtained when these vortices are
absent. This construction is then straightforwardly generalized for arbitrary
d+1 spacetime dimensions. The d=3 case corresponds to the large N chiral
dynamics of SU(N) QCD in the limit $N\rightarrow\infty$.
| [
{
"created": "Wed, 12 Sep 2012 23:17:54 GMT",
"version": "v1"
},
{
"created": "Wed, 26 Dec 2012 16:25:11 GMT",
"version": "v2"
}
] | 2012-12-27 | [
[
"Guimaraes",
"M. S.",
""
],
[
"Rougemont",
"R.",
""
],
[
"Wotzasek",
"C.",
""
],
[
"Zarro",
"C. A. D.",
""
]
] | The Julia-Toulouse approach for condensation of charges and defects is used to show that the bosonized Schwinger model can be obtained through a condensation of electric charges in 1+1 dimensions. The massive model is derived by taking into account the presence of vortices over the electric condensate, while the massless model is obtained when these vortices are absent. This construction is then straightforwardly generalized for arbitrary d+1 spacetime dimensions. The d=3 case corresponds to the large N chiral dynamics of SU(N) QCD in the limit $N\rightarrow\infty$. |
2005.12929 | Paul-Konstantin Oehlmann | Markus Dierigl, Paul-Konstantin Oehlmann and Fabian Ruehle | Non-Simply-Connected Symmetries in 6D SCFTs | 62 pages, 6 figures, 5 tables, 3 appendices | null | 10.1007/JHEP10(2020)173 | CERN-TH-2020-081, UUITP-14/20 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Six-dimensional N=(1,0) superconformal field theories can be engineered
geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We
include torsional sections in the geometry, which lead to a finite Mordell-Weil
group. This allows us to identify the full non-Abelian group structure rather
than just the algebra. The presence of torsion also modifies the center of the
symmetry groups and the matter representations that can appear. This in turn
affects the tensor branch of these theories. We analyze this change for a large
class of superconformal theories with torsion and explicitly construct their
tensor branches. Finally, we elaborate on the connection to the dual heterotic
and M-theory description, in which our configurations are interpreted as
generalizations of discrete holonomy instantons.
| [
{
"created": "Tue, 26 May 2020 18:00:04 GMT",
"version": "v1"
}
] | 2020-12-02 | [
[
"Dierigl",
"Markus",
""
],
[
"Oehlmann",
"Paul-Konstantin",
""
],
[
"Ruehle",
"Fabian",
""
]
] | Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons. |
hep-th/9708018 | Zloshchastiev Konstantin | Konstantin G. Zloshchastiev (Dnepropetrovsk University, Ukraine) | Quantum kink model and SU(2) symmetry: Spin interpretation and
T-violation | 6 pages, LaTeX (IOPP style); final version | J.Phys.A31:6081-6085,1998 | 10.1088/0305-4470/31/28/021 | null | hep-th | null | In this paper we consider the class of exact solutions of the Schrodinger
equation with the Razavi potential. By means of this we obtain some
wavefunctions and mass spectra of the relativistic scalar field model with
spontaneously broken symmetry near the static kink solution. Appearance of the
bosons, which have two different spins, will be shown in the theory, thereby
the additional breaking of discrete symmetry between the quantum mechanical
kink particles with the opposite spins (i.e. the T-violation) takes place.
| [
{
"created": "Tue, 5 Aug 1997 09:18:47 GMT",
"version": "v1"
},
{
"created": "Thu, 2 Jul 1998 15:17:27 GMT",
"version": "v2"
}
] | 2008-11-26 | [
[
"Zloshchastiev",
"Konstantin G.",
"",
"Dnepropetrovsk University, Ukraine"
]
] | In this paper we consider the class of exact solutions of the Schrodinger equation with the Razavi potential. By means of this we obtain some wavefunctions and mass spectra of the relativistic scalar field model with spontaneously broken symmetry near the static kink solution. Appearance of the bosons, which have two different spins, will be shown in the theory, thereby the additional breaking of discrete symmetry between the quantum mechanical kink particles with the opposite spins (i.e. the T-violation) takes place. |
1004.3754 | Martin Richarte MR | Estanislao Herscovich and Mart\'in G. Richarte | Black holes in Einstein-Gauss-Bonnet gravity with a string cloud
background | 13 pages, 5 figures. References added | Phys.Lett.B689:192-200,2010 | 10.1016/j.physletb.2010.04.065 | null | hep-th gr-qc hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We obtain a black hole solution in the Einstein-Gauss-Bonnet theory for the
string cloud model in a five dimensional spacetime. We analyze the event
horizons and naked singularities. Later, we compute the Hawking temperature
$T_{\mathrm{H}}$, the specific heat $C$, the entropy $S$, and the Helmholtz
free energy $F$ of the black hole. The entropy was computed using the Wald
formulation. In addition, the quantum correction to the Wald's entropy is
considered for the string cloud source.
We mainly explore the thermodynamical global and local stability of the
system with vanishing or non-vanishing cosmological constant. The global
thermodynamic phase structure indicates that the Hawking-Page transition is
achieved for this model. Further, we observe that there exist stable black
holes with small radii and that these regions are enlarged when choosing small
values of the string cloud density and of the Gauss-Bonnet parameter. Besides,
the rate of evaporation for these black holes are studied, determining whether
the evaporation time is finite or not. Then, we concentrate on the dynamical
stability of the system, studying the effective potential for s-waves
propagating on the string cloud background.
| [
{
"created": "Wed, 21 Apr 2010 17:47:34 GMT",
"version": "v1"
},
{
"created": "Sun, 5 Sep 2010 00:51:30 GMT",
"version": "v2"
}
] | 2016-08-14 | [
[
"Herscovich",
"Estanislao",
""
],
[
"Richarte",
"Martín G.",
""
]
] | We obtain a black hole solution in the Einstein-Gauss-Bonnet theory for the string cloud model in a five dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature $T_{\mathrm{H}}$, the specific heat $C$, the entropy $S$, and the Helmholtz free energy $F$ of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Wald's entropy is considered for the string cloud source. We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking-Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss-Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background. |
hep-th/9702066 | Serguei Isakov | Serguei B. Isakov, Jon Magne Leinaas, Jan Myrheim, Alexios P.
Polychronakos, Raimund Varnhagen | Algebra of Observables for Identical Particles in One Dimension | 13 pages, Latex, uses epsf, 1 eps figure included | Phys.Lett. B430 (1998) 151-160 | 10.1016/S0370-2693(98)00502-4 | Oslo SHS-96-9, OSLO-TP 4-97 | hep-th cond-mat | null | The algebra of observables for identical particles on a line is formulated
starting from postulated basic commutation relations. A realization of this
algebra in the Calogero model was previously known. New realizations are
presented here in terms of differentiation operators and in terms of
SU(N)-invariant observables of the Hermitian matrix models. Some particular
structure properties of the algebra are briefly discussed.
| [
{
"created": "Fri, 7 Feb 1997 19:24:08 GMT",
"version": "v1"
}
] | 2009-10-30 | [
[
"Isakov",
"Serguei B.",
""
],
[
"Leinaas",
"Jon Magne",
""
],
[
"Myrheim",
"Jan",
""
],
[
"Polychronakos",
"Alexios P.",
""
],
[
"Varnhagen",
"Raimund",
""
]
] | The algebra of observables for identical particles on a line is formulated starting from postulated basic commutation relations. A realization of this algebra in the Calogero model was previously known. New realizations are presented here in terms of differentiation operators and in terms of SU(N)-invariant observables of the Hermitian matrix models. Some particular structure properties of the algebra are briefly discussed. |
hep-th/9805212 | Leonid Chekhov | J. Ambj{\o}rn and L. Chekhov | The NBI matrix model of IIB Superstrings | LaTeX, 11pp | JHEP 9812:007,1998 | 10.1088/1126-6708/1998/12/007 | MIAN-Th-18/98, NBI-HE-98-13, MPS-RR 1998-8 | hep-th | null | We investigate the NBI matrix model with the potential
$X\Lambda+X^{-1}+(2\eta+1)\log X$ recently proposed to describe IIB
superstrings. With the proper normalization, using Virasoro constraints, we
prove the equivalence of this model and the Kontsevich matrix model for
$\eta\ne0$ and find the explicit transformation between the two models.
| [
{
"created": "Fri, 29 May 1998 11:46:33 GMT",
"version": "v1"
}
] | 2014-11-18 | [
[
"Ambjørn",
"J.",
""
],
[
"Chekhov",
"L.",
""
]
] | We investigate the NBI matrix model with the potential $X\Lambda+X^{-1}+(2\eta+1)\log X$ recently proposed to describe IIB superstrings. With the proper normalization, using Virasoro constraints, we prove the equivalence of this model and the Kontsevich matrix model for $\eta\ne0$ and find the explicit transformation between the two models. |
1612.00737 | Mikhail Smolyakov | A.G. Panin, M.N. Smolyakov | Problem with classical stability of U(1) gauged Q-balls | 29 pages, 7 figures, LaTeX. v3: title changed, typos corrected, minor
changes in the text | Phys. Rev. D 95, 065006 (2017) | 10.1103/PhysRevD.95.065006 | INR-TH-2016-043 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we present a detailed study of the problem of classical
stability of U(1) gauged Q-balls. In particular, we show that the standard
methods that are suitable for establishing the classical stability criterion
for ordinary (nongauged) one-field and two-field Q-balls are not effective in
the case of U(1) gauged Q-balls, although all the technical steps of
calculations can be performed in the same way as those for ordinary Q-balls. We
also present the results of numerical simulations in models with different
scalar field potentials, explicitly demonstrating that, in general, the regions
of stability of U(1) gauged Q-balls are not defined in the same way as in the
case of ordinary Q-balls. Consequently, the classical stability criterion for
ordinary Q-balls cannot be applied to U(1) gauged Q-balls in the general case.
| [
{
"created": "Fri, 2 Dec 2016 16:30:47 GMT",
"version": "v1"
},
{
"created": "Thu, 29 Dec 2016 20:35:36 GMT",
"version": "v2"
},
{
"created": "Thu, 9 Mar 2017 17:18:04 GMT",
"version": "v3"
}
] | 2017-03-10 | [
[
"Panin",
"A. G.",
""
],
[
"Smolyakov",
"M. N.",
""
]
] | In this paper, we present a detailed study of the problem of classical stability of U(1) gauged Q-balls. In particular, we show that the standard methods that are suitable for establishing the classical stability criterion for ordinary (nongauged) one-field and two-field Q-balls are not effective in the case of U(1) gauged Q-balls, although all the technical steps of calculations can be performed in the same way as those for ordinary Q-balls. We also present the results of numerical simulations in models with different scalar field potentials, explicitly demonstrating that, in general, the regions of stability of U(1) gauged Q-balls are not defined in the same way as in the case of ordinary Q-balls. Consequently, the classical stability criterion for ordinary Q-balls cannot be applied to U(1) gauged Q-balls in the general case. |
1806.10314 | Matthias Traube | Ralph Blumenhagen, Max Brinkmann, Vladislav Kupriyanov, Matthias
Traube | On the Uniqueness of L$_\infty$ bootstrap: Quasi-isomorphisms are
Seiberg-Witten Maps | 22 pages, v2: references updated, statement of theorem 1 corrected | J.Math.Phys. 59 (2018) no.12, 123505 | 10.1063/1.5048352 | MPP-2018-146 | hep-th math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In the context of the recently proposed L$_\infty$ bootstrap approach, the
question arises whether the so constructed gauge theories are unique solutions
of the L$_\infty$ relations. Physically it is expected that two gauge theories
should be considered equivalent if they are related by a field redefinition
described by a Seiberg-Witten map. To clarify the consequences in the
L$_\infty$ framework, it is proven that Seiberg-Witten maps between physically
equivalent gauge theories correspond to quasi-isomorphisms of the underlying
L$_\infty$ algebras. The proof suggests an extension of the definition of a
Seiberg-Witten map to the closure conditions of two gauge transformations and
the dynamical equations of motion.
| [
{
"created": "Wed, 27 Jun 2018 06:12:57 GMT",
"version": "v1"
},
{
"created": "Mon, 9 Jul 2018 14:01:45 GMT",
"version": "v2"
}
] | 2019-10-25 | [
[
"Blumenhagen",
"Ralph",
""
],
[
"Brinkmann",
"Max",
""
],
[
"Kupriyanov",
"Vladislav",
""
],
[
"Traube",
"Matthias",
""
]
] | In the context of the recently proposed L$_\infty$ bootstrap approach, the question arises whether the so constructed gauge theories are unique solutions of the L$_\infty$ relations. Physically it is expected that two gauge theories should be considered equivalent if they are related by a field redefinition described by a Seiberg-Witten map. To clarify the consequences in the L$_\infty$ framework, it is proven that Seiberg-Witten maps between physically equivalent gauge theories correspond to quasi-isomorphisms of the underlying L$_\infty$ algebras. The proof suggests an extension of the definition of a Seiberg-Witten map to the closure conditions of two gauge transformations and the dynamical equations of motion. |
0911.4708 | Juan Maldacena | Luis F. Alday, Davide Gaiotto and Juan Maldacena | Thermodynamic Bubble Ansatz | 55 pages, 22 figures. v2: references added, V3: small typo fixed | JHEP 1109:032,2011 | 10.1007/JHEP09(2011)032 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Motivated by the computation of scattering amplitudes at strong coupling, we
consider minimal area surfaces in AdS_5 which end on a null polygonal contour
at the boundary. We map the classical problem of finding the surface into an
SU(4) Hitchin system. The polygon with six edges is the first non-trivial
example. For this case, we write an integral equation which determines the area
as a function of the shape of the polygon. The equations are identical to those
of the Thermodynamics Bethe Ansatz. Moreover, the area is given by the free
energy of this TBA system. The high temperature limit of the TBA system can be
exactly solved. It leads to an explicit expression for a special class of
hexagonal contours.
| [
{
"created": "Tue, 24 Nov 2009 20:32:10 GMT",
"version": "v1"
},
{
"created": "Thu, 17 Dec 2009 13:24:18 GMT",
"version": "v2"
},
{
"created": "Tue, 27 Jul 2010 13:35:30 GMT",
"version": "v3"
}
] | 2015-03-13 | [
[
"Alday",
"Luis F.",
""
],
[
"Gaiotto",
"Davide",
""
],
[
"Maldacena",
"Juan",
""
]
] | Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS_5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4) Hitchin system. The polygon with six edges is the first non-trivial example. For this case, we write an integral equation which determines the area as a function of the shape of the polygon. The equations are identical to those of the Thermodynamics Bethe Ansatz. Moreover, the area is given by the free energy of this TBA system. The high temperature limit of the TBA system can be exactly solved. It leads to an explicit expression for a special class of hexagonal contours. |
1806.03690 | Valentin Reys | Bernard de Wit, Sameer Murthy, Valentin Reys | BRST quantization and equivariant cohomology: localization with
asymptotic boundaries | 26 pages | null | 10.1007/JHEP09(2018)084 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We develop BRST quantization of gauge theories with a soft gauge algebra on
spaces with asymptotic boundaries. The asymptotic boundary conditions are
imposed on background fields, while quantum fluctuations about these fields are
described in terms of quantum fields that vanish at the boundary. This leads us
to construct a suitable background field formalism that is generally applicable
to soft gauge algebras, and therefore to supergravity. We define a nilpotent
BRST charge that acts on both the background and the quantum fields, as well as
on the background and quantum ghosts. When the background is restricted to be
invariant under a residual isometry group, the background ghosts must be
restricted accordingly and play the role of the parameters of the background
isometries. Requiring in addition that the background ghosts will be BRST
invariant as well then converts the BRST algebra into an equivariant one. The
background fields and ghosts are then invariant under the equivariant
transformations while the quantum fields and ghosts transform under both the
equivariant and the background transformations. We demonstrate how this
formalism is suitable for carrying out localization calculations in a large
class of theories, including supergravity defined on asymptotic backgrounds
that admit supersymmetry.
| [
{
"created": "Sun, 10 Jun 2018 16:58:49 GMT",
"version": "v1"
}
] | 2018-10-17 | [
[
"de Wit",
"Bernard",
""
],
[
"Murthy",
"Sameer",
""
],
[
"Reys",
"Valentin",
""
]
] | We develop BRST quantization of gauge theories with a soft gauge algebra on spaces with asymptotic boundaries. The asymptotic boundary conditions are imposed on background fields, while quantum fluctuations about these fields are described in terms of quantum fields that vanish at the boundary. This leads us to construct a suitable background field formalism that is generally applicable to soft gauge algebras, and therefore to supergravity. We define a nilpotent BRST charge that acts on both the background and the quantum fields, as well as on the background and quantum ghosts. When the background is restricted to be invariant under a residual isometry group, the background ghosts must be restricted accordingly and play the role of the parameters of the background isometries. Requiring in addition that the background ghosts will be BRST invariant as well then converts the BRST algebra into an equivariant one. The background fields and ghosts are then invariant under the equivariant transformations while the quantum fields and ghosts transform under both the equivariant and the background transformations. We demonstrate how this formalism is suitable for carrying out localization calculations in a large class of theories, including supergravity defined on asymptotic backgrounds that admit supersymmetry. |
1709.04392 | Zhong-Ying Fan | Zhong-Ying Fan | Black holes in vector-tensor theories and their thermodynamics | to appera in EPJC, major revisions, referecens added. 33 pages | null | 10.1140/epjc/s10052-018-5540-7 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we study Einstein gravity either minimally or non-minimally
coupled to a vector field which breaks the gauge symmetry explicitly in general
dimensions. We first consider a minimal theory which is simply the
Einstein-Proca theory extended with a quartic self-interaction term for the
vector field. We obtain its general static maximally symmetric black hole
solution and study the thermodynamics using Wald formalism. The aspects of the
solution are much like a Reissner-Nordstr{\o}m black hole in spite of that a
global charge cannot be defined for the vector. For non-minimal theories, we
obtain a lot of exact black hole solutions, depending on the parameters of the
theories. In particular, many of the solutions are general static and have
maximal symmetry. However, there are some subtleties and ambiguities in the
derivation of the first laws because the existence of an algebraic degree of
freedom of the vector in general invalids the Wald entropy formula. The
thermodynamics of these solutions deserves further studies.
| [
{
"created": "Wed, 13 Sep 2017 15:56:40 GMT",
"version": "v1"
},
{
"created": "Mon, 18 Sep 2017 11:44:29 GMT",
"version": "v2"
},
{
"created": "Fri, 12 Jan 2018 10:48:44 GMT",
"version": "v3"
}
] | 2018-03-14 | [
[
"Fan",
"Zhong-Ying",
""
]
] | In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca theory extended with a quartic self-interaction term for the vector field. We obtain its general static maximally symmetric black hole solution and study the thermodynamics using Wald formalism. The aspects of the solution are much like a Reissner-Nordstr{\o}m black hole in spite of that a global charge cannot be defined for the vector. For non-minimal theories, we obtain a lot of exact black hole solutions, depending on the parameters of the theories. In particular, many of the solutions are general static and have maximal symmetry. However, there are some subtleties and ambiguities in the derivation of the first laws because the existence of an algebraic degree of freedom of the vector in general invalids the Wald entropy formula. The thermodynamics of these solutions deserves further studies. |
hep-th/0507263 | Atsushi Yamaguchi | Nobuyuki Ishibashi, Tsunehide Kuroki and Atsushi Yamaguchi | Universality of Nonperturbative Effects in c<1 Noncritical String Theory | 17 pages | JHEP 0509 (2005) 043 | 10.1088/1126-6708/2005/09/043 | null | hep-th | null | Nonperturbative effects in c<1 noncritical string theory are studied using
the two-matrix model. Such effects are known to have the form fixed by the
string equations but the numerical coefficients have not been known so far.
Using the method proposed recently, we show that it is possible to determine
the coefficients for (p,q) string theory. We find that they are indeed finite
in the double scaling limit and universal in the sense that they do not depend
on the detailed structure of the potential of the two-matrix model.
| [
{
"created": "Wed, 27 Jul 2005 11:40:02 GMT",
"version": "v1"
}
] | 2009-11-11 | [
[
"Ishibashi",
"Nobuyuki",
""
],
[
"Kuroki",
"Tsunehide",
""
],
[
"Yamaguchi",
"Atsushi",
""
]
] | Nonperturbative effects in c<1 noncritical string theory are studied using the two-matrix model. Such effects are known to have the form fixed by the string equations but the numerical coefficients have not been known so far. Using the method proposed recently, we show that it is possible to determine the coefficients for (p,q) string theory. We find that they are indeed finite in the double scaling limit and universal in the sense that they do not depend on the detailed structure of the potential of the two-matrix model. |
hep-th/0410045 | Mingxing Luo | Mingxing Luo and Congkao Wen | One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills
Theories | Minor changes and typos fixed. Published version in JHEP | JHEP0411:004,2004 | 10.1088/1126-6708/2004/11/004 | null | hep-th hep-ph | null | One-loop maximal helicity violating (MHV) amplitudes in N=4 super Yang-Mills
(SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and
Witten (CSW). The relations between leading N_c amplitudes A_{n;1} and
sub-leading amplitudes A_{n;c} obtained by the CSW prescription are found to be
identical to those obtained from conventional field theory calculations.
Combining with existing results, this establishes the validity of the CSW
prescription to one-loop in the calculation of MHV amplitudes in N=4 SYM
theories of finite N_c.
| [
{
"created": "Tue, 5 Oct 2004 14:01:43 GMT",
"version": "v1"
},
{
"created": "Thu, 7 Oct 2004 06:13:39 GMT",
"version": "v2"
},
{
"created": "Sun, 21 Nov 2004 08:08:13 GMT",
"version": "v3"
}
] | 2008-11-26 | [
[
"Luo",
"Mingxing",
""
],
[
"Wen",
"Congkao",
""
]
] | One-loop maximal helicity violating (MHV) amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and Witten (CSW). The relations between leading N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;c} obtained by the CSW prescription are found to be identical to those obtained from conventional field theory calculations. Combining with existing results, this establishes the validity of the CSW prescription to one-loop in the calculation of MHV amplitudes in N=4 SYM theories of finite N_c. |
hep-th/9608084 | null | T.E. Clark and S.T. Love | On the Holomorphic Structure of a Low Energy Supersymmetric Wilson
Effective Action | 10 pages, LaTeX | Phys.Lett. B388 (1996) 577-580 | 10.1016/S0370-2693(96)01188-4 | null | hep-th | null | The Wilson (exact) renormalization group equations are used to determine the
evolution of a general low energy N=1 supersymmetric action containing a U(1)
gauge vector multiplet and a neutral chiral multiplet. The effective theory
evolves towards satisfying a fixed relation where the K\"ahler potential and
effective gauge coupling are obtained from a N=2 supersymmetric holomorphic
prepotential.
| [
{
"created": "Tue, 13 Aug 1996 17:55:09 GMT",
"version": "v1"
}
] | 2009-10-30 | [
[
"Clark",
"T. E.",
""
],
[
"Love",
"S. T.",
""
]
] | The Wilson (exact) renormalization group equations are used to determine the evolution of a general low energy N=1 supersymmetric action containing a U(1) gauge vector multiplet and a neutral chiral multiplet. The effective theory evolves towards satisfying a fixed relation where the K\"ahler potential and effective gauge coupling are obtained from a N=2 supersymmetric holomorphic prepotential. |
hep-th/0306229 | A. N. Ivanov | M. Faber, A. N. Ivanov | On the vacua in the massless Thirring model | 19 pages, 4 figures, Latex | null | null | null | hep-th | null | We calculate the most general effective potential for the massless Thirring
model in dependence of the local fields of all fermion-antifermion collective
excitations. We analyse the minima of this potential describing different vacua
of the quantum system. We confirm the existence of the absolute minimum found
in EPJC 20, 723 (2001) corresponding to the chirally broken phase of the
massless Thirring model. As has been shown in EPJC 20, 723 (2001) this minimum
is stable under quantum fluctuations.
| [
{
"created": "Tue, 24 Jun 2003 13:34:21 GMT",
"version": "v1"
},
{
"created": "Sat, 20 Dec 2003 18:56:35 GMT",
"version": "v2"
}
] | 2007-05-23 | [
[
"Faber",
"M.",
""
],
[
"Ivanov",
"A. N.",
""
]
] | We calculate the most general effective potential for the massless Thirring model in dependence of the local fields of all fermion-antifermion collective excitations. We analyse the minima of this potential describing different vacua of the quantum system. We confirm the existence of the absolute minimum found in EPJC 20, 723 (2001) corresponding to the chirally broken phase of the massless Thirring model. As has been shown in EPJC 20, 723 (2001) this minimum is stable under quantum fluctuations. |
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