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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2109.12351 | Nikhil Kalyanapuram | Nikhil Kalyanapuram | Holographic Representations of Supertranslation Eigenstates | v1: 15 pages, dedicated to the memory of Prof. Steven Weinberg | null | null | null | hep-th hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We construct by direct computation holographic presentations of
supertranslation vacua given a set of supermomenta. To do this, we make use of
two-dimensional dual models recently discovered by the author, which encode
soft dynamics of gravity at leading order. In particular, the two-dimensional
models are used to define soft currents, of which the supertranslation vacua
are eigenstates. Operationally, the eigenstates are determined by the bare
vacuum state dressed by exponential operators that generalize the dressing due
to Faddeev and Kulish.
| [
{
"created": "Sat, 25 Sep 2021 12:27:36 GMT",
"version": "v1"
}
] | 2021-09-28 | [
[
"Kalyanapuram",
"Nikhil",
""
]
] | We construct by direct computation holographic presentations of supertranslation vacua given a set of supermomenta. To do this, we make use of two-dimensional dual models recently discovered by the author, which encode soft dynamics of gravity at leading order. In particular, the two-dimensional models are used to define soft currents, of which the supertranslation vacua are eigenstates. Operationally, the eigenstates are determined by the bare vacuum state dressed by exponential operators that generalize the dressing due to Faddeev and Kulish. |
1603.07679 | Erick J. Weinberg | Ali Masoumi, Sonia Paban, and Erick J. Weinberg | Tunneling from a Minkowski vacuum to an AdS vacuum: A new thin-wall
regime | 29 pages, 13 figures; added discussion, figures, and references | Phys. Rev. D 94, 025023 (2016) | 10.1103/PhysRevD.94.025023 | UTTG-02-16 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Using numerical and analytic methods, we study quantum tunneling from a
Minkowski false vacuum to an anti-de Sitter true vacuum. Scanning the parameter
space of theories with quartic and non-polynomial potentials, we find that for
any given potential tunneling is completely quenched if gravitational effects
are made sufficiently strong. For potentials where $\epsilon$, the energy
density difference between the vacua, is small compared to the barrier height,
this occurs in the thin-wall regime studied by Coleman and De Luccia. However,
we find that other potentials, possibly with $\epsilon$ much greater than the
barrier height, produce a new type of thin-wall bounce when gravitational
effects become strong. We show that the critical curve that bounds the region
in parameter space where the false vacuum is stable can be found by a
computationally simple overshoot/undershoot argument. We discuss the treatment
of boundary terms in the bounce calculation and show that, with proper
regularization, one obtains an identical finite result for the tunneling
exponent regardless of whether or not these are included. Finally, we briefly
discuss the extension of our results to transitions between anti-de Sitter
vacua.
| [
{
"created": "Thu, 24 Mar 2016 17:46:32 GMT",
"version": "v1"
},
{
"created": "Mon, 25 Jul 2016 19:51:14 GMT",
"version": "v2"
}
] | 2016-07-26 | [
[
"Masoumi",
"Ali",
""
],
[
"Paban",
"Sonia",
""
],
[
"Weinberg",
"Erick J.",
""
]
] | Using numerical and analytic methods, we study quantum tunneling from a Minkowski false vacuum to an anti-de Sitter true vacuum. Scanning the parameter space of theories with quartic and non-polynomial potentials, we find that for any given potential tunneling is completely quenched if gravitational effects are made sufficiently strong. For potentials where $\epsilon$, the energy density difference between the vacua, is small compared to the barrier height, this occurs in the thin-wall regime studied by Coleman and De Luccia. However, we find that other potentials, possibly with $\epsilon$ much greater than the barrier height, produce a new type of thin-wall bounce when gravitational effects become strong. We show that the critical curve that bounds the region in parameter space where the false vacuum is stable can be found by a computationally simple overshoot/undershoot argument. We discuss the treatment of boundary terms in the bounce calculation and show that, with proper regularization, one obtains an identical finite result for the tunneling exponent regardless of whether or not these are included. Finally, we briefly discuss the extension of our results to transitions between anti-de Sitter vacua. |
2006.07290 | Oscar Loaiza-Brito | Nana Cabo Bizet, Cesar Damian, Oscar Loaiza-Brito, Dami\'an Kaloni
Mayorga Pe\~na and J.A. Monta\~nez-Barrera | Testing Swampland Conjectures with Machine Learning | 30 pages, 14 Figures. (v2) References added | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider Type IIB compactifications on an isotropic torus $T^6$ threaded
by geometric and non geometric fluxes. For this particular setup we apply
supervised machine learning techniques, namely an artificial neural network
coupled to a genetic algorithm, in order to obtain more than sixty thousand
flux configurations yielding to a scalar potential with at least one critical
point. We observe that both stable AdS vacua with large moduli masses and small
vacuum energy as well as unstable dS vacua with small tachyonic mass and large
energy are absent, in accordance to the Refined de Sitter Conjecture. Moreover,
by considering a hierarchy among fluxes, we observe that perturbative solutions
with small values for the vacuum energy and moduli masses are favored, as well
as scenarios in which the lightest modulus mass is much greater than the
corresponding AdS vacuum scale. Finally we apply some results on Random Matrix
Theory to conclude that the most probable mass spectrum derived from this
string setup is that satisfying the Refined de Sitter and AdS scale
conjectures.
| [
{
"created": "Fri, 12 Jun 2020 16:12:17 GMT",
"version": "v1"
},
{
"created": "Mon, 29 Jun 2020 17:10:58 GMT",
"version": "v2"
}
] | 2020-06-30 | [
[
"Bizet",
"Nana Cabo",
""
],
[
"Damian",
"Cesar",
""
],
[
"Loaiza-Brito",
"Oscar",
""
],
[
"Peña",
"Damián Kaloni Mayorga",
""
],
[
"Montañez-Barrera",
"J. A.",
""
]
] | We consider Type IIB compactifications on an isotropic torus $T^6$ threaded by geometric and non geometric fluxes. For this particular setup we apply supervised machine learning techniques, namely an artificial neural network coupled to a genetic algorithm, in order to obtain more than sixty thousand flux configurations yielding to a scalar potential with at least one critical point. We observe that both stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the Refined de Sitter Conjecture. Moreover, by considering a hierarchy among fluxes, we observe that perturbative solutions with small values for the vacuum energy and moduli masses are favored, as well as scenarios in which the lightest modulus mass is much greater than the corresponding AdS vacuum scale. Finally we apply some results on Random Matrix Theory to conclude that the most probable mass spectrum derived from this string setup is that satisfying the Refined de Sitter and AdS scale conjectures. |
2009.02450 | Jiakang Bao | Jiakang Bao, Yang-Hui He, Yan Xiao | Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases | 49 pages; v3: minor corrections | J. High Energ. Phys. 2021, 203 (2021) | 10.1007/JHEP01(2021)203 | null | hep-th math.AG | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study chiral rings of 4d $\mathcal{N}=1$ supersymmetric gauge theories via
the notion of K-stability. We show that when using Hilbert series to perform
the computations of Futaki invariants, it is not enough to only include the
test symmetry information in the former's denominator. We discuss a way to
modify the numerator so that K-stability can be correctly determined, and a
rescaling method is also applied to simplify the calculations involving test
configurations. All of these are illustrated with a host of examples, by
considering vacuum moduli spaces of various theories. Using Gr\"obner basis and
plethystic techniques, many non-complete intersections can also be addressed,
thus expanding the list of known theories in the literature.
| [
{
"created": "Sat, 5 Sep 2020 03:15:57 GMT",
"version": "v1"
},
{
"created": "Thu, 24 Sep 2020 12:00:51 GMT",
"version": "v2"
},
{
"created": "Sat, 19 Dec 2020 20:26:45 GMT",
"version": "v3"
}
] | 2021-05-20 | [
[
"Bao",
"Jiakang",
""
],
[
"He",
"Yang-Hui",
""
],
[
"Xiao",
"Yan",
""
]
] | We study chiral rings of 4d $\mathcal{N}=1$ supersymmetric gauge theories via the notion of K-stability. We show that when using Hilbert series to perform the computations of Futaki invariants, it is not enough to only include the test symmetry information in the former's denominator. We discuss a way to modify the numerator so that K-stability can be correctly determined, and a rescaling method is also applied to simplify the calculations involving test configurations. All of these are illustrated with a host of examples, by considering vacuum moduli spaces of various theories. Using Gr\"obner basis and plethystic techniques, many non-complete intersections can also be addressed, thus expanding the list of known theories in the literature. |
2005.04250 | Yin-Chen He | Yin-Chen He, Junchen Rong, and Ning Su | Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the
deconfined phase transition to a putative new family of CFTs | 16+3 pages | SciPost Phys. 10, 115 (2021) | 10.21468/SciPostPhys.10.5.115 | null | hep-th cond-mat.str-el | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | It is well established that the $O(N)$ Wilson-Fisher (WF) CFT sits at a kink
of the numerical bounds from bootstrapping four point function of $O(N)$
vector. Moving away from the WF kinks, there indeed exists another family of
kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different
from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the
non-WF kinks exist in arbitrary dimensions but only for a large enough
$N>N_c(d)$ in a given dimension $d$. In this paper we have achieved a thorough
understanding for few special cases of these non-WF kinks. The first case is
the $O(4)$ bootstrap in 2d, where the non-WF kink turns out to be the $SU(2)_1$
Wess-Zumino-Witten (WZW) model, and all the $SU(2)_{k>2}$ WZW models saturate
the numerical bound on the left side of the kink. We further carry out
dimensional continuation of the 2d $SU(2)_1$ kink towards the 3d $SO(5)$
deconfined phase transition. We find the kink disappears at around $d=2.7$
dimensions indicating the $SO(5)$ deconfined phase transition is weakly first
order. The second interesting observation is, the $O(2)$ bootstrap bound does
not show any kink in 2d ($N_c=2$), but is surprisingly saturated by the 2d free
boson CFT (also called Luttinger liquid) all the way on the numerical curve.
The last case is the $N=\infty$ limit, where the non-WF kink sits at
$(\Delta_\phi, \Delta_T)=(d-1, 2d)$ in $d$ dimensions. We manage to write down
its analytical four point function in arbitrary dimensions, which equals to the
subtraction of correlation functions of a free fermion theory and generalized
free theory. An important feature of this solution is the existence of a full
tower of conserved higher spin current. We speculate that a new family of CFTs
will emerge at non-WF kinks for finite $N$, in a similar fashion as $O(N)$ WF
CFTs originating from free boson at $N=\infty$.
| [
{
"created": "Fri, 8 May 2020 18:18:34 GMT",
"version": "v1"
},
{
"created": "Mon, 1 Jun 2020 00:32:27 GMT",
"version": "v2"
},
{
"created": "Tue, 13 Apr 2021 23:17:22 GMT",
"version": "v3"
}
] | 2021-05-26 | [
[
"He",
"Yin-Chen",
""
],
[
"Rong",
"Junchen",
""
],
[
"Su",
"Ning",
""
]
] | It is well established that the $O(N)$ Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of $O(N)$ vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough $N>N_c(d)$ in a given dimension $d$. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks. The first case is the $O(4)$ bootstrap in 2d, where the non-WF kink turns out to be the $SU(2)_1$ Wess-Zumino-Witten (WZW) model, and all the $SU(2)_{k>2}$ WZW models saturate the numerical bound on the left side of the kink. We further carry out dimensional continuation of the 2d $SU(2)_1$ kink towards the 3d $SO(5)$ deconfined phase transition. We find the kink disappears at around $d=2.7$ dimensions indicating the $SO(5)$ deconfined phase transition is weakly first order. The second interesting observation is, the $O(2)$ bootstrap bound does not show any kink in 2d ($N_c=2$), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the $N=\infty$ limit, where the non-WF kink sits at $(\Delta_\phi, \Delta_T)=(d-1, 2d)$ in $d$ dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite $N$, in a similar fashion as $O(N)$ WF CFTs originating from free boson at $N=\infty$. |
2209.06222 | Rodolfo Panerai | Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara | The phase diagram of $T\bar{T}$-deformed Yang-Mills theory on the sphere | 25 pages, 3 figures | null | 10.1007/JHEP11(2022)078 | UUITP-38/22 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the large-$N$ dynamics of $T\bar{T}$-deformed two-dimensional
Yang-Mills theory at genus zero. The 1/$N$-expansion of the free energy is
obtained by exploiting the associated flow equation and the complete phase
diagram of the theory is derived for both signs of the rescaled deformation
parameter $\tau$. We observe a third-order phase transition driven by instanton
condensation, which is the deformed version of the familiar Douglas-Kazakov
transition separating the weakly-coupled from the strongly-coupled phase. By
studying said phases, we compute the deformation of both the perturbative
sector and the Gross-Taylor string expansion. Nonperturbative corrections in
$\tau$ drive the system into an unexplored disordered phase separated by a
novel critical line meeting tangentially the Douglas-Kazakov one at a
tricritical point. The associated phase transition is induced by the collision
of large-$N$ saddle points, determining its second-order character.
| [
{
"created": "Tue, 13 Sep 2022 18:00:01 GMT",
"version": "v1"
}
] | 2022-11-30 | [
[
"Griguolo",
"Luca",
""
],
[
"Panerai",
"Rodolfo",
""
],
[
"Papalini",
"Jacopo",
""
],
[
"Seminara",
"Domenico",
""
]
] | We study the large-$N$ dynamics of $T\bar{T}$-deformed two-dimensional Yang-Mills theory at genus zero. The 1/$N$-expansion of the free energy is obtained by exploiting the associated flow equation and the complete phase diagram of the theory is derived for both signs of the rescaled deformation parameter $\tau$. We observe a third-order phase transition driven by instanton condensation, which is the deformed version of the familiar Douglas-Kazakov transition separating the weakly-coupled from the strongly-coupled phase. By studying said phases, we compute the deformation of both the perturbative sector and the Gross-Taylor string expansion. Nonperturbative corrections in $\tau$ drive the system into an unexplored disordered phase separated by a novel critical line meeting tangentially the Douglas-Kazakov one at a tricritical point. The associated phase transition is induced by the collision of large-$N$ saddle points, determining its second-order character. |
2205.07930 | Matthew Buican | Chinmaya Bhargava, Matthew Buican, and Hongliang Jiang | On the Protected Spectrum of the Minimal Argyres-Douglas Theory | 34 pages and 2 appendices; v2: references added and typos corrected | null | 10.1007/JHEP08(2022)132 | QMUL-PH-22-17 | hep-th | http://creativecommons.org/licenses/by/4.0/ | Despite the power of supersymmetry, finding exact closed-form expressions for
the protected operator spectra of interacting superconformal field theories
(SCFTs) is difficult. In this paper, we take a step towards a solution for the
"simplest" interacting 4D $\mathcal{N}=2$ SCFT: the minimal Argyres-Douglas
(MAD) theory. We present two results that go beyond the well-understood Coulomb
branch and Schur sectors. First, we find the exact closed-form spectrum of
multiplets containing operators that are chiral with respect to any
$\mathcal{N}=1\subset\mathcal{N}=2$ superconformal subalgebra. We argue that
this "full" chiral sector (FCS) is as simple as allowed by unitarity for a
theory with a Coulomb branch and that, up to a rescaling of $U(1)_r$ quantum
numbers and the vanishing of a finite number of states, the MAD FCS is
isospectral to the FCS of the free $\mathcal{N}=2$ Abelian gauge theory. In the
language of superconformal representation theory, this leaves only the spectrum
of the poorly understood $\bar{\mathcal{C}}_{R,r(j,\bar j)}$ multiplets to be
determined. Our second result sheds light on these observables: we find an
exact closed-form answer for the number of $\bar{\mathcal{C}}_{0,r(j,0)}$
multiplets, for any $r$ and $j$, in the MAD theory. We argue that this
sub-sector is also as simple as allowed by unitarity for a theory with a
Coulomb branch and that there is a natural map to the corresponding sector of
the free $\mathcal{N}=2$ Abelian gauge theory. These results motivate a
conjecture on the full local operator algebra of the MAD theory.
| [
{
"created": "Mon, 16 May 2022 18:29:44 GMT",
"version": "v1"
},
{
"created": "Thu, 16 Jun 2022 13:31:52 GMT",
"version": "v2"
}
] | 2022-09-07 | [
[
"Bhargava",
"Chinmaya",
""
],
[
"Buican",
"Matthew",
""
],
[
"Jiang",
"Hongliang",
""
]
] | Despite the power of supersymmetry, finding exact closed-form expressions for the protected operator spectra of interacting superconformal field theories (SCFTs) is difficult. In this paper, we take a step towards a solution for the "simplest" interacting 4D $\mathcal{N}=2$ SCFT: the minimal Argyres-Douglas (MAD) theory. We present two results that go beyond the well-understood Coulomb branch and Schur sectors. First, we find the exact closed-form spectrum of multiplets containing operators that are chiral with respect to any $\mathcal{N}=1\subset\mathcal{N}=2$ superconformal subalgebra. We argue that this "full" chiral sector (FCS) is as simple as allowed by unitarity for a theory with a Coulomb branch and that, up to a rescaling of $U(1)_r$ quantum numbers and the vanishing of a finite number of states, the MAD FCS is isospectral to the FCS of the free $\mathcal{N}=2$ Abelian gauge theory. In the language of superconformal representation theory, this leaves only the spectrum of the poorly understood $\bar{\mathcal{C}}_{R,r(j,\bar j)}$ multiplets to be determined. Our second result sheds light on these observables: we find an exact closed-form answer for the number of $\bar{\mathcal{C}}_{0,r(j,0)}$ multiplets, for any $r$ and $j$, in the MAD theory. We argue that this sub-sector is also as simple as allowed by unitarity for a theory with a Coulomb branch and that there is a natural map to the corresponding sector of the free $\mathcal{N}=2$ Abelian gauge theory. These results motivate a conjecture on the full local operator algebra of the MAD theory. |
hep-th/0305176 | Thomas Fischbacher | Thomas Fischbacher | Mapping the vacuum structure of gauged maximal supergravities: an
application of high-performance symbolic algebra | PhD thesis, 140 pages, 11 figures | null | null | AEI-2003-046 | hep-th cs.SC | null | The analysis of the extremal structure of the scalar potentials of gauged
maximally extended supergravity models in five, four, and three dimensions, and
hence the determination of possible vacuum states of these models is a
computationally challenging task due to the occurrence of the exceptional Lie
groups $E_6$, $E_7$, $E_8$ in the definition of these potentials. At present,
the most promising approach to gain information about nontrivial vacua of these
models is to perform a truncation of the potential to submanifolds of the $G/H$
coset manifold of scalars which are invariant under a subgroup of the gauge
group and of sufficiently low dimension to make an analytic treatment possible.
New tools are presented which allow a systematic and highly effective study
of these potentials up to a previously unreached level of complexity. Explicit
forms of new truncations of the potentials of four- and three-dimensional
models are given, and for N=16, D=3 supergravities, which are much more rich in
structure than their higher-dimensional cousins, a series of new nontrivial
vacua is identified and analysed.
| [
{
"created": "Tue, 20 May 2003 13:42:15 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Fischbacher",
"Thomas",
""
]
] | The analysis of the extremal structure of the scalar potentials of gauged maximally extended supergravity models in five, four, and three dimensions, and hence the determination of possible vacuum states of these models is a computationally challenging task due to the occurrence of the exceptional Lie groups $E_6$, $E_7$, $E_8$ in the definition of these potentials. At present, the most promising approach to gain information about nontrivial vacua of these models is to perform a truncation of the potential to submanifolds of the $G/H$ coset manifold of scalars which are invariant under a subgroup of the gauge group and of sufficiently low dimension to make an analytic treatment possible. New tools are presented which allow a systematic and highly effective study of these potentials up to a previously unreached level of complexity. Explicit forms of new truncations of the potentials of four- and three-dimensional models are given, and for N=16, D=3 supergravities, which are much more rich in structure than their higher-dimensional cousins, a series of new nontrivial vacua is identified and analysed. |
1401.4723 | Marc Schiereck | Min-xin Huang, Albrecht Klemm, Jonas Reuter, Marc Schiereck | Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit | 53 pages, 8 figures | null | 10.1007/JHEP02(2015)031 | USTC-ICTS-14-03, Bonn-TH-2014-02 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We use mirror symmetry, quantum geometry and modularity properties of
elliptic curves to calculate the refined free energies in the
Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on
del Pezzo surfaces. Quantum geometry here is to be understood as a quantum
deformed version of rigid special geometry, which has its origin in the quantum
mechanical behaviour of branes in the topological string B-model. We will argue
that, in the Seiberg-Witten picture, only the Coulomb parameters lead to
quantum corrections, while the mass parameters remain uncorrected. In certain
cases we will also compute the expansion of the free energies at the orbifold
point and the conifold locus. We will compute the quantum corrections order by
order on $\hbar$, by deriving second order differential operators, which act on
the classical periods.
| [
{
"created": "Sun, 19 Jan 2014 19:32:38 GMT",
"version": "v1"
}
] | 2015-06-18 | [
[
"Huang",
"Min-xin",
""
],
[
"Klemm",
"Albrecht",
""
],
[
"Reuter",
"Jonas",
""
],
[
"Schiereck",
"Marc",
""
]
] | We use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum geometry here is to be understood as a quantum deformed version of rigid special geometry, which has its origin in the quantum mechanical behaviour of branes in the topological string B-model. We will argue that, in the Seiberg-Witten picture, only the Coulomb parameters lead to quantum corrections, while the mass parameters remain uncorrected. In certain cases we will also compute the expansion of the free energies at the orbifold point and the conifold locus. We will compute the quantum corrections order by order on $\hbar$, by deriving second order differential operators, which act on the classical periods. |
2208.14710 | Fl\'ora Enik\H{o} G\'eg\'eny | F. G\'eg\'eny, S. Nagy, K. Sailer | On the Lorentz symmetry in conformally reduced Quantum Gravity | 11 pages, 7 figures | null | 10.1088/1361-6382/acafd1 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The functional renormalization group treatment of the conform reduced
Einstein-Hilbert gravity is extended by following the evolution of the time and
space derivatives separately, in order to consider the Lorentz symmetry during
the evolution. We found the Reuter fixed point in the ultraviolet region. It is
shown that starting from the Gaussian fixed point the Lorentz symmetry breaks
down in the vicinity of the Reuter fixed point. Similarly, in the symmetry
broken phase it also breaks down in the infrared region close to a critical
singularity scale. By calculating the anomalous dimension form the kinetic term
of the action, we found a new relevant coupling belonging to the curvature.
| [
{
"created": "Wed, 31 Aug 2022 09:17:04 GMT",
"version": "v1"
}
] | 2023-02-01 | [
[
"Gégény",
"F.",
""
],
[
"Nagy",
"S.",
""
],
[
"Sailer",
"K.",
""
]
] | The functional renormalization group treatment of the conform reduced Einstein-Hilbert gravity is extended by following the evolution of the time and space derivatives separately, in order to consider the Lorentz symmetry during the evolution. We found the Reuter fixed point in the ultraviolet region. It is shown that starting from the Gaussian fixed point the Lorentz symmetry breaks down in the vicinity of the Reuter fixed point. Similarly, in the symmetry broken phase it also breaks down in the infrared region close to a critical singularity scale. By calculating the anomalous dimension form the kinetic term of the action, we found a new relevant coupling belonging to the curvature. |
hep-th/0005238 | Danuta Karczewska | D. Karczewska, R. Manka (University of Silesia) | Monopole in the dilatonic gauge field theory | latex4, 15 pages with 3 figures (eps), to appear in Austr. J. of
Phys. Vol. 53, 5 | Austral.J.Phys. 53 (2000) 5 | null | ; AstroUSL-2000-3 | hep-th | null | A numerical study of coupled to the dilaton field, static, spherically
symmetric monopole solutions inspired by the Kaluza-Klein theory with large
extra dimensions are presented. The generalized Prasad-Sommerfield solution is
obtained. We show that monopole may have also the dilaton cloud configurations.
| [
{
"created": "Thu, 25 May 2000 14:07:16 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Karczewska",
"D.",
"",
"University of Silesia"
],
[
"Manka",
"R.",
"",
"University of Silesia"
]
] | A numerical study of coupled to the dilaton field, static, spherically symmetric monopole solutions inspired by the Kaluza-Klein theory with large extra dimensions are presented. The generalized Prasad-Sommerfield solution is obtained. We show that monopole may have also the dilaton cloud configurations. |
1612.03169 | Angel Ballesteros | Angel Ballesteros, Francisco J. Herranz, Fabio Musso, Pedro Naranjo | The kappa-(A)dS quantum algebra in (3+1) dimensions | 13 pages | Phys. Lett. B 766 (2017) 205-211 | 10.1016/j.physletb.2017.01.020 | null | hep-th gr-qc math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The quantum duality principle is used to obtain explicitly the Poisson
analogue of the kappa-(A)dS quantum algebra in (3+1) dimensions as the
corresponding Poisson-Lie structure on the dual solvable Lie group. The
construction is fully performed in a kinematical basis and deformed Casimir
functions are also explicitly obtained. The cosmological constant $\Lambda$ is
included as a Poisson-Lie group contraction parameter, and the limit
$\Lambda\to 0$ leads to the well-known kappa-Poincar\'e algebra in the
bicrossproduct basis. A twisted version with Drinfel'd double structure of this
kappa-(A)dS deformation is sketched.
| [
{
"created": "Fri, 9 Dec 2016 11:39:38 GMT",
"version": "v1"
}
] | 2017-01-19 | [
[
"Ballesteros",
"Angel",
""
],
[
"Herranz",
"Francisco J.",
""
],
[
"Musso",
"Fabio",
""
],
[
"Naranjo",
"Pedro",
""
]
] | The quantum duality principle is used to obtain explicitly the Poisson analogue of the kappa-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson-Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant $\Lambda$ is included as a Poisson-Lie group contraction parameter, and the limit $\Lambda\to 0$ leads to the well-known kappa-Poincar\'e algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this kappa-(A)dS deformation is sketched. |
2405.10189 | Vasileios Vergioglou | Anatoly Konechny, Vasileios Vergioglou | On fusing matrices associated with conformal boundary conditions | LaTex, 80 pages | null | null | null | hep-th math-ph math.CT math.MP | http://creativecommons.org/licenses/by/4.0/ | In the context of rational conformal field theories (RCFT) we look at the
fusing matrices that arise when a topological defect is attached to a conformal
boundary condition. We call such junctions open topological defects. One type
of fusing matrices arises when two open defects fuse while another arises when
an open defect passes through a boundary operator. We use the topological field
theory approach to RCFTs based on Frobenius algebra objects in modular tensor
categories to describe the general structure associated with such matrices and
how to compute them from a given Frobenius algebra object and its
representation theory. We illustrate the computational process on the rational
free boson theories. Applications to boundary renormalisation group flows are
briefly discussed.
| [
{
"created": "Thu, 16 May 2024 15:33:13 GMT",
"version": "v1"
},
{
"created": "Fri, 14 Jun 2024 12:14:12 GMT",
"version": "v2"
},
{
"created": "Fri, 12 Jul 2024 12:29:41 GMT",
"version": "v3"
}
] | 2024-07-15 | [
[
"Konechny",
"Anatoly",
""
],
[
"Vergioglou",
"Vasileios",
""
]
] | In the context of rational conformal field theories (RCFT) we look at the fusing matrices that arise when a topological defect is attached to a conformal boundary condition. We call such junctions open topological defects. One type of fusing matrices arises when two open defects fuse while another arises when an open defect passes through a boundary operator. We use the topological field theory approach to RCFTs based on Frobenius algebra objects in modular tensor categories to describe the general structure associated with such matrices and how to compute them from a given Frobenius algebra object and its representation theory. We illustrate the computational process on the rational free boson theories. Applications to boundary renormalisation group flows are briefly discussed. |
hep-th/0007046 | null | Luca Mezincescu | Star Operation in Quantum Mechanics | misprints corrected, additional references | null | null | UMTG-233 | hep-th | null | We outline the description of Quantum Mechanics with noncommuting coordinates
within the framework of star operation. We discuss simple cases of
integrability.
| [
{
"created": "Thu, 6 Jul 2000 22:52:03 GMT",
"version": "v1"
},
{
"created": "Fri, 21 Jul 2000 04:10:51 GMT",
"version": "v2"
}
] | 2007-05-23 | [
[
"Mezincescu",
"Luca",
""
]
] | We outline the description of Quantum Mechanics with noncommuting coordinates within the framework of star operation. We discuss simple cases of integrability. |
1410.2860 | Aram Saharian | E.R. Bezerra de Mello, A.A. Saharian, V. Vardanyan | Induced vacuum currents in anti-de Sitter space with toral dimensions | 15 pages, 4 figures | Phys. Lett. B 741 (2015) 155 | 10.1016/j.physletb.2014.12.036 | null | hep-th gr-qc quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We investigate the Hadamard function and the vacuum expectation value of the
current density for a charged massive scalar field on a slice of anti-de Sitter
(AdS) space described in Poincar\'{e} coordinates with toroidally compact
dimensions. Along compact dimensions periodicity conditions are imposed on the
field with general phases. Moreover, the presence of a constant gauge field is
assumed. The latter gives rise to Aharonov-Bohm-like effects on the vacuum
currents. The current density along compact dimensions is a periodic function
of the gauge field flux with the period equal to the flux quantum. It vanishes
on the AdS boundary and, near the horizon, to the leading order, it is
conformally related to the corresponding quantity in Minkowski bulk for a
massless field. For large values of the length of the compact dimension
compared with the AdS curvature radius, the vacuum current decays as power-law
for both massless and massive fields. This behavior is essentially different
from from the corresponding one in Minkowski background, where the currents for
a massive field are suppressed exponentially.
| [
{
"created": "Wed, 24 Sep 2014 18:04:30 GMT",
"version": "v1"
}
] | 2014-12-31 | [
[
"de Mello",
"E. R. Bezerra",
""
],
[
"Saharian",
"A. A.",
""
],
[
"Vardanyan",
"V.",
""
]
] | We investigate the Hadamard function and the vacuum expectation value of the current density for a charged massive scalar field on a slice of anti-de Sitter (AdS) space described in Poincar\'{e} coordinates with toroidally compact dimensions. Along compact dimensions periodicity conditions are imposed on the field with general phases. Moreover, the presence of a constant gauge field is assumed. The latter gives rise to Aharonov-Bohm-like effects on the vacuum currents. The current density along compact dimensions is a periodic function of the gauge field flux with the period equal to the flux quantum. It vanishes on the AdS boundary and, near the horizon, to the leading order, it is conformally related to the corresponding quantity in Minkowski bulk for a massless field. For large values of the length of the compact dimension compared with the AdS curvature radius, the vacuum current decays as power-law for both massless and massive fields. This behavior is essentially different from from the corresponding one in Minkowski background, where the currents for a massive field are suppressed exponentially. |
0708.4414 | Axel Krause | Axel Krause | Large Gravitational Waves and Lyth Bound in Multi Brane Inflation | 15 pages, 1 figure; v2: references added; v3: final version published
in JCAP | JCAP 0807:001,2008 | 10.1088/1475-7516/2008/07/001 | LMU-ASC 64/07 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | It is shown that multi M5-brane inflation in heterotic M-theory gives rise to
a detectable gravitational wave power spectrum with tensor fraction $r$
typically larger than the projected experimental sensitivity, $r_{exp} = 0.01$.
A measurable gravitational wave power spectrum entails a large inflationary
energy scale and a super-Planckian inflaton variation. They present serious
problems for particle theory model building resp. a reliable effective field
theory description. These problems are eased or even absent in multi-brane
inflation models and multi M5-brane inflation, in particular.
| [
{
"created": "Fri, 31 Aug 2007 19:49:37 GMT",
"version": "v1"
},
{
"created": "Tue, 18 Sep 2007 10:35:41 GMT",
"version": "v2"
},
{
"created": "Tue, 30 Sep 2008 11:14:00 GMT",
"version": "v3"
}
] | 2009-06-11 | [
[
"Krause",
"Axel",
""
]
] | It is shown that multi M5-brane inflation in heterotic M-theory gives rise to a detectable gravitational wave power spectrum with tensor fraction $r$ typically larger than the projected experimental sensitivity, $r_{exp} = 0.01$. A measurable gravitational wave power spectrum entails a large inflationary energy scale and a super-Planckian inflaton variation. They present serious problems for particle theory model building resp. a reliable effective field theory description. These problems are eased or even absent in multi-brane inflation models and multi M5-brane inflation, in particular. |
2010.07861 | Donal O'Connell | William T. Emond, Yu-tin Huang, Uri Kol, Nathan Moynihan and Donal
O'Connell | Amplitudes from Coulomb to Kerr-Taub-NUT | 35 pages + appendices, 2 figures. Mathematica notebook attached | null | null | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Electric-magnetic duality, the Newman-Janis shift, and the double copy all
act by elementary operations on three-point amplitudes. At the same time, they
generate a network of interesting classical solutions spanning from the Coulomb
charge via the dyon to the Kerr-Taub-NUT spacetime. We identify the amplitudes
corresponding to each of these solutions, working to all orders in spin, but to
leading perturbative order. We confirm that the amplitudes double-copy when the
solutions are related by the classical double copy. Along the way we show that
the Kerr-Taub-NUT solution corresponds to a gravitational electric-magnetic
duality rotation acting on the Kerr solution, again to all orders in spin, and
demonstrate that the asymptotic charges also transform simply under our
operations.
| [
{
"created": "Thu, 15 Oct 2020 16:26:41 GMT",
"version": "v1"
},
{
"created": "Sun, 18 Oct 2020 17:04:22 GMT",
"version": "v2"
}
] | 2020-10-20 | [
[
"Emond",
"William T.",
""
],
[
"Huang",
"Yu-tin",
""
],
[
"Kol",
"Uri",
""
],
[
"Moynihan",
"Nathan",
""
],
[
"O'Connell",
"Donal",
""
]
] | Electric-magnetic duality, the Newman-Janis shift, and the double copy all act by elementary operations on three-point amplitudes. At the same time, they generate a network of interesting classical solutions spanning from the Coulomb charge via the dyon to the Kerr-Taub-NUT spacetime. We identify the amplitudes corresponding to each of these solutions, working to all orders in spin, but to leading perturbative order. We confirm that the amplitudes double-copy when the solutions are related by the classical double copy. Along the way we show that the Kerr-Taub-NUT solution corresponds to a gravitational electric-magnetic duality rotation acting on the Kerr solution, again to all orders in spin, and demonstrate that the asymptotic charges also transform simply under our operations. |
2106.04851 | Yin Jiang | Tian Xu and Yin Jiang | Proca equation and vector field quantization in rotating system | 7 pages, 0 figures | null | 10.1088/1674-1137/ac1d9c | null | hep-th hep-ph nucl-th | http://creativecommons.org/licenses/by/4.0/ | A strong background field will change the vacuum structure and the proper
basis of a system drastically in both classical and quantum mechanics, e.g. the
Landau levels in a background magnetic field. The situation is the same for the
rotating case. In such a system the usual set of plane-wave states would no
longer be suitable as a starting point of perturbation. Alternatively and
straightforwardly in a rapidly and globally rotating system, it is better to
reformulate the perturbation computation in principle. In this work we will
complete the first step for the spin-1 field, which includes solving the Proca
equation in present of a background rotation and complete its canonical
quantization. It will be shown that because of the symmetry the eigen states
are actually the same as the ones of Maxwell equations in cylindrical
coordinate. The propagator as well as the near-central approximation will be
obtained by considering the vorticity areas are so small in the relativistic
QGP.
| [
{
"created": "Wed, 9 Jun 2021 07:17:31 GMT",
"version": "v1"
}
] | 2021-11-17 | [
[
"Xu",
"Tian",
""
],
[
"Jiang",
"Yin",
""
]
] | A strong background field will change the vacuum structure and the proper basis of a system drastically in both classical and quantum mechanics, e.g. the Landau levels in a background magnetic field. The situation is the same for the rotating case. In such a system the usual set of plane-wave states would no longer be suitable as a starting point of perturbation. Alternatively and straightforwardly in a rapidly and globally rotating system, it is better to reformulate the perturbation computation in principle. In this work we will complete the first step for the spin-1 field, which includes solving the Proca equation in present of a background rotation and complete its canonical quantization. It will be shown that because of the symmetry the eigen states are actually the same as the ones of Maxwell equations in cylindrical coordinate. The propagator as well as the near-central approximation will be obtained by considering the vorticity areas are so small in the relativistic QGP. |
hep-th/0612222 | Niklas Johansson | Ulf H. Danielsson, Niklas Johansson and Magdalena Larfors | The world next door - Results in landscape topography | 27 pages latex, 19 figures | JHEP 0703:080,2007 | 10.1088/1126-6708/2007/03/080 | UITTP-23/06 | hep-th | null | Recently, it has become clear that neighboring multiple vacua might have
interesting consequences for the physics of the early universe. In this paper
we investigate the topography of the string landscape corresponding to complex
structure moduli of flux compactified type IIB string theory. We find that
series of continuously connected vacua are common. The properties of these
series are described, and we relate the existence of infinite series of minima
to certain unresolved mathematical problems in group theory. Numerical studies
of the mirror quintic serve as illustrating examples.
| [
{
"created": "Wed, 20 Dec 2006 16:27:35 GMT",
"version": "v1"
}
] | 2010-10-27 | [
[
"Danielsson",
"Ulf H.",
""
],
[
"Johansson",
"Niklas",
""
],
[
"Larfors",
"Magdalena",
""
]
] | Recently, it has become clear that neighboring multiple vacua might have interesting consequences for the physics of the early universe. In this paper we investigate the topography of the string landscape corresponding to complex structure moduli of flux compactified type IIB string theory. We find that series of continuously connected vacua are common. The properties of these series are described, and we relate the existence of infinite series of minima to certain unresolved mathematical problems in group theory. Numerical studies of the mirror quintic serve as illustrating examples. |
hep-th/9609060 | Hasan Karadayi | H. R. Karadayi and M. Gungormez | An Explicit Construction of Casimir Operators and Eigenvalues : I | 14 pages, no figures, revised version, to appear in Jour.Math.Phys | J.Math.Phys. 38 (1997) 5976-5990 | 10.1063/1.532175 | itu-hep 96-01 | hep-th alg-geom math-ph math.AG math.MP | null | We give a general method to construct a complete set of linearly independent
Casimir operators of a Lie algebra with rank N. For a Casimir operator of
degree p, this will be provided by an explicit calculation of its symmetric
coefficients $ g^{A_1,A_2,.. A_p}$. It is seen that these coefficients can be
descibed by some rational polinomials of rank N. These polinomials are also
multilinear in Cartan sub-algebra indices taking values from the set $I_0 =
{1,2,.. N}$. The crucial point here is that for each degree one needs, in
general, more than one polinomials. This in fact is related with an observation
that the whole set of symmetric coefficients $ g^{A_1,A_2,.. A_p} $ is
decomposed into sum subsets which are in one to one correspondence with these
polinomials. We call these subsets clusters and introduce some indicators with
which we specify different clusters. These indicators determine all the
clusters whatever the numerical values of coefficients $g^{A_1,A_2,.. A_p}$
are. For any degree p, the number of clusters is independent of rank N. This
hence allows us to generalize our results to any value of rank N.
To specify the general framework explicit constructions of 4th and 5th order
Casimir operators of $A_N$ Lie algebras are studied and all the polinomials
which specify the numerical value of their coefficients are given explicitly.
| [
{
"created": "Sat, 7 Sep 1996 15:06:49 GMT",
"version": "v1"
},
{
"created": "Wed, 25 Sep 1996 15:05:09 GMT",
"version": "v2"
},
{
"created": "Fri, 10 Jan 1997 15:22:45 GMT",
"version": "v3"
},
{
"created": "Wed, 18 Jun 1997 13:15:19 GMT",
"version": "v4"
}
] | 2009-10-30 | [
[
"Karadayi",
"H. R.",
""
],
[
"Gungormez",
"M.",
""
]
] | We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients $ g^{A_1,A_2,.. A_p}$. It is seen that these coefficients can be descibed by some rational polinomials of rank N. These polinomials are also multilinear in Cartan sub-algebra indices taking values from the set $I_0 = {1,2,.. N}$. The crucial point here is that for each degree one needs, in general, more than one polinomials. This in fact is related with an observation that the whole set of symmetric coefficients $ g^{A_1,A_2,.. A_p} $ is decomposed into sum subsets which are in one to one correspondence with these polinomials. We call these subsets clusters and introduce some indicators with which we specify different clusters. These indicators determine all the clusters whatever the numerical values of coefficients $g^{A_1,A_2,.. A_p}$ are. For any degree p, the number of clusters is independent of rank N. This hence allows us to generalize our results to any value of rank N. To specify the general framework explicit constructions of 4th and 5th order Casimir operators of $A_N$ Lie algebras are studied and all the polinomials which specify the numerical value of their coefficients are given explicitly. |
2407.03698 | Hossein Babaei-Aghbolagh | H. Babaei-Aghbolagh, Song He, Hao Ouyang | Generalized $T\overline{T}$-like Deformations in Duality-Invariant
Nonlinear Electrodynamic Theories | 25 pages, 1 figure | null | null | null | hep-th | http://creativecommons.org/licenses/by-nc-sa/4.0/ | This study introduces a high-order perturbation methodology to categorize two
primary solution types within duality-invariant nonlinear electrodynamic
theories, adhering to the differential self-duality criterion. The first
solution type aligns with irrelevant stress tensor flows, resembling $T\bar{T}$
dynamics, and the second involves a blend of irrelevant $T\bar{T}$-like and
marginal root-$T\bar{T}$-like deformations. Our approach facilitates the
investigation of diverse duality-invariant nonlinear electrodynamics theories
and their stress tensor flows and confirms the commutativity of flows initiated
by irrelevant and marginal operators.
| [
{
"created": "Thu, 4 Jul 2024 07:38:10 GMT",
"version": "v1"
}
] | 2024-07-08 | [
[
"Babaei-Aghbolagh",
"H.",
""
],
[
"He",
"Song",
""
],
[
"Ouyang",
"Hao",
""
]
] | This study introduces a high-order perturbation methodology to categorize two primary solution types within duality-invariant nonlinear electrodynamic theories, adhering to the differential self-duality criterion. The first solution type aligns with irrelevant stress tensor flows, resembling $T\bar{T}$ dynamics, and the second involves a blend of irrelevant $T\bar{T}$-like and marginal root-$T\bar{T}$-like deformations. Our approach facilitates the investigation of diverse duality-invariant nonlinear electrodynamics theories and their stress tensor flows and confirms the commutativity of flows initiated by irrelevant and marginal operators. |
hep-th/0104187 | Vladimir Akulov | V. Akulov | Non-linear way to Supersymmetry and N-extended SUSY | 9 pages | Nucl.Phys.Proc.Suppl.101:15-19,2001 | 10.1016/S0920-5632(01)01488-8 | null | hep-th | null | In this report I give the short historical review some of the first steps
that were done to the invention of SUSY in Kharkov team headed by D.Volkov.
This paper is dedicated to the memory of Prof. Yu. Gol'fand, whose ideas of
SUSY inspired the most active developments in High Energy Physics over thirty
years.
| [
{
"created": "Mon, 23 Apr 2001 13:08:38 GMT",
"version": "v1"
}
] | 2010-05-28 | [
[
"Akulov",
"V.",
""
]
] | In this report I give the short historical review some of the first steps that were done to the invention of SUSY in Kharkov team headed by D.Volkov. This paper is dedicated to the memory of Prof. Yu. Gol'fand, whose ideas of SUSY inspired the most active developments in High Energy Physics over thirty years. |
1509.01305 | Wen-Yu Wen | Wen-Yu Wen, Shang-Yu Wu | Black hole remnant in asymptotic Anti-de Sitter space | 13 pages, 5 figures, submitted version | Eur. Phys. J. C, 75 12 (2015) 608 | 10.1140/epjc/s10052-015-3841-7 | CYCU-HEP-15-06 | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | It is known that a solution of remnant were suggested for black hole ground
state after surface gravity is corrected by loop quantum effect. On the other
hand, a Schwarzschild black hole in asymptotic Anti-de Sitter space would
tunnel into the thermal soliton solution known as the Hawking-Page phase
transition. In this letter, we investigate the low temperature phase of
three-dimensional BTZ black hole and four-dimensional AdS Schwarzschild black
hole. We find that the thermal soliton is energetically favored than the
remnant solution at low temperature in three dimensions, while Planck-size
remnant is still possible in four dimensions. Though the BTZ remnant seems
energetically disfavored, we argue that it is still possible to be found in the
overcooled phase if strings were present and its implication is discussed.
| [
{
"created": "Thu, 3 Sep 2015 23:02:45 GMT",
"version": "v1"
},
{
"created": "Mon, 14 Dec 2015 15:51:31 GMT",
"version": "v2"
}
] | 2015-12-29 | [
[
"Wen",
"Wen-Yu",
""
],
[
"Wu",
"Shang-Yu",
""
]
] | It is known that a solution of remnant were suggested for black hole ground state after surface gravity is corrected by loop quantum effect. On the other hand, a Schwarzschild black hole in asymptotic Anti-de Sitter space would tunnel into the thermal soliton solution known as the Hawking-Page phase transition. In this letter, we investigate the low temperature phase of three-dimensional BTZ black hole and four-dimensional AdS Schwarzschild black hole. We find that the thermal soliton is energetically favored than the remnant solution at low temperature in three dimensions, while Planck-size remnant is still possible in four dimensions. Though the BTZ remnant seems energetically disfavored, we argue that it is still possible to be found in the overcooled phase if strings were present and its implication is discussed. |
hep-th/9803169 | Oliver Haschke | Oliver Haschke, Werner Ruehl | Exactly solvable dynamical systems in the neighborhood of the Calogero
model | 23 pages, 2 figures, replaced and enlarged version | Int.J.Mod.Phys. A14 (1999) 387-408 | 10.1142/S0217751X99000191 | KL-TH 98-03 | hep-th | null | The Hamiltonian of the $N$-particle Calogero model can be expressed in terms
of generators of a Lie algebra for a definite class of representations.
Maintaining this Lie algebra, its representations, and the flatness of the
Riemannian metric belonging to the second order differential operator, the set
of all possible quadratic Lie algebra forms is investigated. For N=3 and N=4
such forms are constructed explicitly and shown to correspond to exactly
solvable Sutherland models. The results can be carried over easily to all $N$.
| [
{
"created": "Fri, 20 Mar 1998 15:01:49 GMT",
"version": "v1"
},
{
"created": "Mon, 27 Apr 1998 09:35:16 GMT",
"version": "v2"
}
] | 2009-10-31 | [
[
"Haschke",
"Oliver",
""
],
[
"Ruehl",
"Werner",
""
]
] | The Hamiltonian of the $N$-particle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For N=3 and N=4 such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all $N$. |
hep-th/9707178 | Tekin Dereli | A. H. Bilge, T. Dereli, S.Kocak | Seiberg-Witten Equations on R^8 | 7 pages, Latex file. No figures. Published in the Proceedings of 5th
Gokova Geometry-Topology Conference | Turk.J.Math.21:87-92,1997 | null | null | hep-th | null | We show that there are no nontrivial solutions of the Seiberg-Witten
equations on R^8 with constant standard spin^c structure.
| [
{
"created": "Mon, 21 Jul 1997 13:20:39 GMT",
"version": "v1"
}
] | 2011-04-20 | [
[
"Bilge",
"A. H.",
""
],
[
"Dereli",
"T.",
""
],
[
"Kocak",
"S.",
""
]
] | We show that there are no nontrivial solutions of the Seiberg-Witten equations on R^8 with constant standard spin^c structure. |
2105.12067 | Harriet Apel | Harriet Apel, Tamara Kohler, Toby Cubitt | Holographic duality between local Hamiltonians from random tensor
networks | 42 pages, 4 figures. v4: updated to published version, expanded
introduction and new figure demonstrating simulation composition | J. High Energ. Phys. 2022, 52 | 10.1007/JHEP03(2022)052 | null | hep-th quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The AdS/CFT correspondence realises the holographic principle where
information in the bulk of a space is encoded at its border. We are yet a long
way from a full mathematical construction of AdS/CFT, but toy models in the
form of holographic quantum error correcting codes (HQECC) have replicated some
interesting features of the correspondence. In this work we construct new
HQECCs built from random stabilizer tensors that describe a duality between
models encompassing local Hamiltonians whilst exactly obeying the
Ryu-Takayanagi entropy formula for all boundary regions. We also obtain
complementary recovery of local bulk operators for any boundary bipartition.
Existing HQECCs have been shown to exhibit these properties individually,
whereas our mathematically rigorous toy models capture these features of
AdS/CFT simultaneously, advancing further towards a complete construction of
holographic duality.
| [
{
"created": "Tue, 25 May 2021 16:48:31 GMT",
"version": "v1"
},
{
"created": "Thu, 29 Jul 2021 07:27:16 GMT",
"version": "v2"
},
{
"created": "Thu, 9 Sep 2021 16:49:18 GMT",
"version": "v3"
},
{
"created": "Wed, 20 Apr 2022 13:06:30 GMT",
"version": "v4"
}
] | 2022-04-21 | [
[
"Apel",
"Harriet",
""
],
[
"Kohler",
"Tamara",
""
],
[
"Cubitt",
"Toby",
""
]
] | The AdS/CFT correspondence realises the holographic principle where information in the bulk of a space is encoded at its border. We are yet a long way from a full mathematical construction of AdS/CFT, but toy models in the form of holographic quantum error correcting codes (HQECC) have replicated some interesting features of the correspondence. In this work we construct new HQECCs built from random stabilizer tensors that describe a duality between models encompassing local Hamiltonians whilst exactly obeying the Ryu-Takayanagi entropy formula for all boundary regions. We also obtain complementary recovery of local bulk operators for any boundary bipartition. Existing HQECCs have been shown to exhibit these properties individually, whereas our mathematically rigorous toy models capture these features of AdS/CFT simultaneously, advancing further towards a complete construction of holographic duality. |
hep-th/0611257 | Orfeu Bertolami | Catarina Bastos, Orfeu Bertolami, Nuno Costa Dias, Jo\~ao Nuno Prata | Weyl-Wigner Formulation of Noncommutative Quantum Mechanics | Revtex4, 3 diagrams, 32 pages | J.Math.Phys.49:072101,2008 | 10.1063/1.2944996 | DM/IST-6.2006 | hep-th | null | We address the phase space formulation of a noncommutative extension of
quantum mechanics in arbitrary dimension, displaying both spatial and momentum
noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner
transform and to the Seiberg-Witten map we construct an isomorphism between the
operator and the phase space representations of the extended Heisenberg
algebra. This map provides a systematic approach to derive the entire structure
of noncommutative quantum mechanics in phase space. We construct the extended
starproduct, Moyal bracket and propose a general definition of noncommutative
states. We study the dynamical and eigenvalue equations of the theory and prove
that the entire formalism is independent of the particular choice of
Seiberg-Witten map. Our approach unifies and generalizes all the previous
proposals for the phase space formulation of noncommutative quantum mechanics.
For concreteness we rederive these proposals by restricting our formalism to
some 2-dimensional spaces.
| [
{
"created": "Thu, 23 Nov 2006 20:53:24 GMT",
"version": "v1"
}
] | 2008-11-26 | [
[
"Bastos",
"Catarina",
""
],
[
"Bertolami",
"Orfeu",
""
],
[
"Dias",
"Nuno Costa",
""
],
[
"Prata",
"João Nuno",
""
]
] | We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Seiberg-Witten map we construct an isomorphism between the operator and the phase space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended starproduct, Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of Seiberg-Witten map. Our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics. For concreteness we rederive these proposals by restricting our formalism to some 2-dimensional spaces. |
1805.11627 | Ran Yacoby | Ran Yacoby | Scalar Correlators in Bosonic Chern-Simons Vector Models | 26 pages, 4 figures | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider the planar limit of Chern-Simons theories coupled to a scalar
$\phi$ in the fundamental representation of a $U(N)_k$ gauge group, at both the
regular and Wilson-Fisher conformal points. These theories have one
single-trace scalar operator $J_0=\phi^{\dagger}\phi$. We calculate its
connected planar $n$-point functions, when all the external momenta are
collinear. More specifically, we derive an algebraic recurrence relation that
expresses each such $n$-point function in terms of lower-point ones. As an
application, we study the four-point function, which was recently shown to be
completely fixed up to three truncated solutions to the conformal bootstrap. We
show that those truncated solutions do not contribute in our bosonic
Chern-Simons theories. The result matches a recent calculation of the
four-point function in Chern-Simons theories coupled to a fermion, providing a
new test of 3d bosonization duality.
| [
{
"created": "Tue, 29 May 2018 18:00:18 GMT",
"version": "v1"
}
] | 2018-05-31 | [
[
"Yacoby",
"Ran",
""
]
] | We consider the planar limit of Chern-Simons theories coupled to a scalar $\phi$ in the fundamental representation of a $U(N)_k$ gauge group, at both the regular and Wilson-Fisher conformal points. These theories have one single-trace scalar operator $J_0=\phi^{\dagger}\phi$. We calculate its connected planar $n$-point functions, when all the external momenta are collinear. More specifically, we derive an algebraic recurrence relation that expresses each such $n$-point function in terms of lower-point ones. As an application, we study the four-point function, which was recently shown to be completely fixed up to three truncated solutions to the conformal bootstrap. We show that those truncated solutions do not contribute in our bosonic Chern-Simons theories. The result matches a recent calculation of the four-point function in Chern-Simons theories coupled to a fermion, providing a new test of 3d bosonization duality. |
0707.4011 | Jonathan Heckman | Jonathan J. Heckman and Cumrun Vafa | Geometrically Induced Phase Transitions at Large N | 47 pages, 7 figures | JHEP0804:052,2008 | 10.1088/1126-6708/2008/04/052 | null | hep-th | null | Utilizing the large N dual description of a metastable system of branes and
anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau
threefold, we study phase transitions induced by changing the positions of the
S^2's. At leading order in 1/N the effective potential for this system is
computed by the planar limit of an auxiliary matrix model. Beginning at the two
loop correction, the degenerate vacuum energy density of the discrete confining
vacua split, and a potential is generated for the axion. Changing the relative
positions of the S^2's causes discrete jumps in the energetically preferred
confining vacuum and can also obstruct direct brane/anti-brane annihilation
processes. The branes must hop to nearby S^2's before annihilating, thus
significantly increasing the lifetime of the corresponding non-supersymmetric
vacua. We also speculate that misaligned metastable glueball phases may
generate a repulsive inter-brane force which stabilizes the radial mode present
in compact Calabi-Yau threefolds.
| [
{
"created": "Fri, 27 Jul 2007 13:51:52 GMT",
"version": "v1"
}
] | 2008-11-26 | [
[
"Heckman",
"Jonathan J.",
""
],
[
"Vafa",
"Cumrun",
""
]
] | Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2's. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2's causes discrete jumps in the energetically preferred confining vacuum and can also obstruct direct brane/anti-brane annihilation processes. The branes must hop to nearby S^2's before annihilating, thus significantly increasing the lifetime of the corresponding non-supersymmetric vacua. We also speculate that misaligned metastable glueball phases may generate a repulsive inter-brane force which stabilizes the radial mode present in compact Calabi-Yau threefolds. |
1012.4393 | Daniel Thompson | Daniel C. Thompson | T-duality Invariant Approaches to String Theory | PhD Thesis; 148 pages | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This thesis investigates the quantum properties of T-duality invariant
formalisms of String Theory. We introduce and review duality invariant
formalisms of String Theory including the Doubled Formalism. We calculate the
background field equations for the Doubled Formalism of Abelian T-duality and
show how they are consistent with those of a conventional String Theory
description of a toroidal compactification. We generalise these considerations
to the case of Poisson--Lie T-duality and show that the system of
renormalisation group equations obtained from the duality invariant parent
theory are equivalent to those of either of the T-dual pair of sigma-models. In
duality invariant formalisms it is quite common to loose manifest Lorentz
invariance at the level of the Lagrangian. The lack of manifest invariance
means that at the quantum level one might anticipate Lorentz anomalies and we
show that such anomalies cancel non-trivially. These represent important and
non-trivial consistency checks of the duality invariant approach to String
Theory.
| [
{
"created": "Mon, 20 Dec 2010 16:38:01 GMT",
"version": "v1"
}
] | 2010-12-21 | [
[
"Thompson",
"Daniel C.",
""
]
] | This thesis investigates the quantum properties of T-duality invariant formalisms of String Theory. We introduce and review duality invariant formalisms of String Theory including the Doubled Formalism. We calculate the background field equations for the Doubled Formalism of Abelian T-duality and show how they are consistent with those of a conventional String Theory description of a toroidal compactification. We generalise these considerations to the case of Poisson--Lie T-duality and show that the system of renormalisation group equations obtained from the duality invariant parent theory are equivalent to those of either of the T-dual pair of sigma-models. In duality invariant formalisms it is quite common to loose manifest Lorentz invariance at the level of the Lagrangian. The lack of manifest invariance means that at the quantum level one might anticipate Lorentz anomalies and we show that such anomalies cancel non-trivially. These represent important and non-trivial consistency checks of the duality invariant approach to String Theory. |
2107.10720 | Kiyoharu Kawana | Hikaru Kawai and Kiyoharu Kawana | Multi-critical point principle as the origin of classical conformality
and its generalizations | 23 pages, 4 figures; version to appear in PTEP (v2) | null | null | null | hep-th hep-ph | http://creativecommons.org/licenses/by/4.0/ | Multi-critical point principle (MPP) is one of the interesting theoretical
possibilities that can explain the fine-tuning problems of the Universe. It
simply claims that "the coupling constants of a theory are tuned to one of the
multi-critical points, where some of the extrema of the effective potential are
degenerate." One of the simplest examples is the vanishing of the second
derivative of the effective potential around a minimum. This corresponds to the
so-called classical conformality, because it implies that the renormalized mass
$m^2$ vanishes. More generally, the form of the effective potential of a model
depends on several coupling constants, and we should sweep them to find all the
multi-critical points. In this paper, we study the multi-critical points of a
general scalar field $\phi$ at one-loop level under the circumstance that the
vacuum expectation values of the other fields are all zero. For simplicity, we
also assume that the other fields are either massless or so heavy that they do
not contribute to the low energy effective potential of $\phi$. This assumption
makes our discussion very simple because the resultant one-loop effective
potential is parametrized by only four effective couplings. Although our
analysis is not completely general because of the assumption, it still can be
widely applicable to many models of the Coleman-Weinberg mechanism and its
generalizations. After classifying the multi-critical points at low-energy
scales, we will briefly mention the possibility of criticalities at high-energy
scales and their implications for cosmology.
| [
{
"created": "Thu, 22 Jul 2021 14:53:41 GMT",
"version": "v1"
},
{
"created": "Wed, 5 Jan 2022 05:52:39 GMT",
"version": "v2"
}
] | 2022-01-06 | [
[
"Kawai",
"Hikaru",
""
],
[
"Kawana",
"Kiyoharu",
""
]
] | Multi-critical point principle (MPP) is one of the interesting theoretical possibilities that can explain the fine-tuning problems of the Universe. It simply claims that "the coupling constants of a theory are tuned to one of the multi-critical points, where some of the extrema of the effective potential are degenerate." One of the simplest examples is the vanishing of the second derivative of the effective potential around a minimum. This corresponds to the so-called classical conformality, because it implies that the renormalized mass $m^2$ vanishes. More generally, the form of the effective potential of a model depends on several coupling constants, and we should sweep them to find all the multi-critical points. In this paper, we study the multi-critical points of a general scalar field $\phi$ at one-loop level under the circumstance that the vacuum expectation values of the other fields are all zero. For simplicity, we also assume that the other fields are either massless or so heavy that they do not contribute to the low energy effective potential of $\phi$. This assumption makes our discussion very simple because the resultant one-loop effective potential is parametrized by only four effective couplings. Although our analysis is not completely general because of the assumption, it still can be widely applicable to many models of the Coleman-Weinberg mechanism and its generalizations. After classifying the multi-critical points at low-energy scales, we will briefly mention the possibility of criticalities at high-energy scales and their implications for cosmology. |
1905.03076 | Pietro Longhi | Wei Li and Pietro Longhi | Gluing two affine Yangians of $\mathfrak{gl}_1$ | 88 pages, 12 figures | null | 10.1007/JHEP10(2019)131 | null | hep-th math.QA math.RT | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We construct a four-parameter family of affine Yangian algebras by gluing two
copies of the affine Yangian of $\mathfrak{gl}_1$. Our construction allows for
gluing operators with arbitrary (integer or half integer) conformal dimension
and arbitrary (bosonic or fermionic) statistics, which is related to the
relative framing. The resulting family of algebras is a two-parameter
generalization of the $\mathcal{N}=2$ affine Yangian, which is isomorphic to
the universal enveloping algebra of $\mathfrak{u}(1)\oplus
\mathcal{W}^{\mathcal{N}=2}_{\infty}[\lambda]$. All algebras that we construct
have natural representations in terms of "twin plane partitions", a pair of
plane partitions appropriately joined along one common leg. We observe that the
geometry of twin plane partitions, which determines the algebra, bears striking
similarities to the geometry of certain toric Calabi-Yau threefolds.
| [
{
"created": "Wed, 8 May 2019 14:11:21 GMT",
"version": "v1"
}
] | 2020-01-08 | [
[
"Li",
"Wei",
""
],
[
"Longhi",
"Pietro",
""
]
] | We construct a four-parameter family of affine Yangian algebras by gluing two copies of the affine Yangian of $\mathfrak{gl}_1$. Our construction allows for gluing operators with arbitrary (integer or half integer) conformal dimension and arbitrary (bosonic or fermionic) statistics, which is related to the relative framing. The resulting family of algebras is a two-parameter generalization of the $\mathcal{N}=2$ affine Yangian, which is isomorphic to the universal enveloping algebra of $\mathfrak{u}(1)\oplus \mathcal{W}^{\mathcal{N}=2}_{\infty}[\lambda]$. All algebras that we construct have natural representations in terms of "twin plane partitions", a pair of plane partitions appropriately joined along one common leg. We observe that the geometry of twin plane partitions, which determines the algebra, bears striking similarities to the geometry of certain toric Calabi-Yau threefolds. |
1311.1105 | Sunyoung Shin | Sunyoung Shin | $T^3$ deformations and $\beta$-deformed geometries | 11 pages. Final version, incorporating the referee corrections | Phys. Rev. D 89, 065026 (2014) | 10.1103/PhysRevD.89.065026 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We discuss $\beta$-deformed geometries on two types of $T^3$'s where the
direction along the third coordinate is not orthogonal to the direction along
the second coordinate or the direction along the first coordinate. We show that
the intersection angle between the direction along the third coordinate and the
direction along the second coordinate corresponds to the parameter of the
S-duality of the $\beta$-deformation while the intersection angle between the
direction along the third coordinate and the direction along the first
coordinate generalizes the $\beta$-deformed geometry.
| [
{
"created": "Tue, 5 Nov 2013 16:07:23 GMT",
"version": "v1"
},
{
"created": "Wed, 19 Mar 2014 18:36:37 GMT",
"version": "v2"
}
] | 2014-03-26 | [
[
"Shin",
"Sunyoung",
""
]
] | We discuss $\beta$-deformed geometries on two types of $T^3$'s where the direction along the third coordinate is not orthogonal to the direction along the second coordinate or the direction along the first coordinate. We show that the intersection angle between the direction along the third coordinate and the direction along the second coordinate corresponds to the parameter of the S-duality of the $\beta$-deformation while the intersection angle between the direction along the third coordinate and the direction along the first coordinate generalizes the $\beta$-deformed geometry. |
hep-th/0502111 | Vijay Balasubramanian | Vijay Balasubramanian, Klaus Larjo, Joan Simon | Much Ado About Nothing | LaTeX, 26 pages, 3 eps figures | Class.Quant.Grav. 22 (2005) 4149-4170 | 10.1088/0264-9381/22/19/023 | UPR-1110-T | hep-th | null | We describe the semiclassical decay of a class of orbifolds of AdS space via
a bubble of nothing. The bounce is the small Euclidean AdS-Schwarzschild
solution. The negative cosmological constant introduces subtle features in the
conservation of energy during the decay. A near-horizon limit of D3-branes in
the Milne orbifold spacetime gives rise to our false vacuum. Conversely, a
focusing limit in the latter produces flat space compactified on a circle. The
dual field theory description involves a novel analytic continuation of the
thermal partition function of Yang-Mills theory on a three-sphere times a
circle.
| [
{
"created": "Fri, 11 Feb 2005 19:15:48 GMT",
"version": "v1"
}
] | 2009-11-11 | [
[
"Balasubramanian",
"Vijay",
""
],
[
"Larjo",
"Klaus",
""
],
[
"Simon",
"Joan",
""
]
] | We describe the semiclassical decay of a class of orbifolds of AdS space via a bubble of nothing. The bounce is the small Euclidean AdS-Schwarzschild solution. The negative cosmological constant introduces subtle features in the conservation of energy during the decay. A near-horizon limit of D3-branes in the Milne orbifold spacetime gives rise to our false vacuum. Conversely, a focusing limit in the latter produces flat space compactified on a circle. The dual field theory description involves a novel analytic continuation of the thermal partition function of Yang-Mills theory on a three-sphere times a circle. |
0902.1847 | Andrey Slavnov A | A.A.Slavnov | Lorentz invariant quantization of the Yang-Mills theory free of Gribov
ambiguity | 8 pages,no figures | Theor.Math.Phys.161:1497-1502,2009 | 10.1007/s11232-009-0136-x | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A new fomulation of the Yang-Mills theory which allows to avoid the problem
of Gribov ambiguity of the gauge fixing is proposed.
| [
{
"created": "Wed, 11 Feb 2009 10:55:31 GMT",
"version": "v1"
}
] | 2014-11-18 | [
[
"Slavnov",
"A. A.",
""
]
] | A new fomulation of the Yang-Mills theory which allows to avoid the problem of Gribov ambiguity of the gauge fixing is proposed. |
1208.2182 | Lorenzo Battarra | Lorenzo Battarra, George Lavrelashvili and Jean-Luc Lehners | Negative Modes of Oscillating Instantons | 21 pages, 7 figures | null | 10.1103/PhysRevD.86.124001 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We investigate in detail the properties of oscillating instanton solutions
discussed recently in the literature. We find that the solutions with N nodes
contain exactly N homogeneous negative modes in their spectrum of linear
perturbations. The existence of extra negative modes for the N > 1 solutions
suggest that they are not final state physical objects resulting from
tunneling, but rather unstable intermediate thermal configurations. By
contrast, the single negative mode for the N = 1 instanton confirms its
interpretation as mediating the curved-space tunneling between vacua with equal
energy densities.
| [
{
"created": "Fri, 10 Aug 2012 14:12:37 GMT",
"version": "v1"
},
{
"created": "Thu, 8 Nov 2012 15:31:03 GMT",
"version": "v2"
}
] | 2013-05-30 | [
[
"Battarra",
"Lorenzo",
""
],
[
"Lavrelashvili",
"George",
""
],
[
"Lehners",
"Jean-Luc",
""
]
] | We investigate in detail the properties of oscillating instanton solutions discussed recently in the literature. We find that the solutions with N nodes contain exactly N homogeneous negative modes in their spectrum of linear perturbations. The existence of extra negative modes for the N > 1 solutions suggest that they are not final state physical objects resulting from tunneling, but rather unstable intermediate thermal configurations. By contrast, the single negative mode for the N = 1 instanton confirms its interpretation as mediating the curved-space tunneling between vacua with equal energy densities. |
2006.13234 | Andrea Placidi | Gianluca Grignani, Troels Harmark, Marta Orselli, Andrea Placidi | Fixing the non-relativistic expansion of the 1PM potential | 20 pages | null | 10.1007/JHEP12(2020)142 | null | hep-th gr-qc hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We obtain a first order post-Minkowskian two-body effective potential whose
post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann
potential. Post-Minkowskian potentials can be extracted from on-shell
scattering amplitudes in a quantum field theory of scalar matter coupled to
gravity. Previously, such potentials did not reproduce the
Einstein-Infeld-Hoffmann potential without employing a suitable canonical
transformation. In this work, we resolve this issue by obtaining a new
expression for the first-order post-Minkowskian potential. This is accomplished
by exploiting the reference frame dependence that arises in the scattering
amplitude computation. Finally, as a check on our result, we demonstrate that
our new potential gives the correct scattering angle.
| [
{
"created": "Tue, 23 Jun 2020 18:00:07 GMT",
"version": "v1"
}
] | 2021-02-03 | [
[
"Grignani",
"Gianluca",
""
],
[
"Harmark",
"Troels",
""
],
[
"Orselli",
"Marta",
""
],
[
"Placidi",
"Andrea",
""
]
] | We obtain a first order post-Minkowskian two-body effective potential whose post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann potential. Post-Minkowskian potentials can be extracted from on-shell scattering amplitudes in a quantum field theory of scalar matter coupled to gravity. Previously, such potentials did not reproduce the Einstein-Infeld-Hoffmann potential without employing a suitable canonical transformation. In this work, we resolve this issue by obtaining a new expression for the first-order post-Minkowskian potential. This is accomplished by exploiting the reference frame dependence that arises in the scattering amplitude computation. Finally, as a check on our result, we demonstrate that our new potential gives the correct scattering angle. |
1008.3836 | Klaus Bering | Igor A. Batalin and Klaus Bering | Path Integral Formulation with Deformed Antibracket | 13 pages, LaTeX. v2: Added references. To appear in Phys. Lett. B | Phys.Lett.B694:158-166,2010 | 10.1016/j.physletb.2010.09.047 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We propose how to incorporate the Leites-Shchepochkina-Konstein-Tyutin
deformed antibracket into the quantum field-antifield formalism.
| [
{
"created": "Mon, 23 Aug 2010 15:24:26 GMT",
"version": "v1"
},
{
"created": "Mon, 20 Sep 2010 15:32:10 GMT",
"version": "v2"
}
] | 2011-03-28 | [
[
"Batalin",
"Igor A.",
""
],
[
"Bering",
"Klaus",
""
]
] | We propose how to incorporate the Leites-Shchepochkina-Konstein-Tyutin deformed antibracket into the quantum field-antifield formalism. |
2011.14121 | Evgenii Ievlev | E. Ievlev | Dynamics of non-Abelian strings in supersymmetric gauge theories | 200 pages; PhD thesis, SPbSU and PNPI; English version, full text at
go.spbu.ru/20a2711 | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This thesis is devoted to studying strong coupling phenomena (and confinement
in particular) in supersymmetric gauge theories. The central object of
investigation is the non-Abelian string that is responsible for the
"instead-of-confinement" phase for monopoles in 4D ${\mathcal N} = 2$
supersymmetric QCD with the U($N$) gauge group and $N_f$ flavors of quark
hypermultiplets, $N \leqslant N_f \leqslant 2 N$.
Here it is shown that the non-Abelian strings and confined monopoles survive
when we transition to the ${\mathcal N} = 1$ supersymmetric QCD. To this end we
consider a mass term $\mu$ for the adjoint matter, and in the limit of large
$\mu$ the bulk theory flows to ${\mathcal N} = 1$. We consider this transition
both from the bulk point of view and from the world sheet theory, which is the
two-dimensional $\mathbb{CP}(N-1)$ model. Survival of monopoles in the
${\mathcal N} = 1$ supersymmetric QCD is important for the
"instead-of-confinement" phase, and also for the Seiberg-Witten picture of
confinement.
Apart from that, we also consider non-Abelian vortex strings in 4D
$\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$
flavors of quark hypermultiplets. It has been recently shown that these
vortices behave as critical superstrings. In particular, the lowest string
state appears to be a massless BPS "baryon." Here we show the occurrence of
this stringy baryon using a purely field-theoretic method. Moreover, we
explicitly demonstrate the "instead-of-confinement" phase, when the screened
quarks and gauge bosons of weak coupling are replaced by the confined
monopole-antimonopole pairs of strong coupling.
English version. Full text (Russian and English) is available at the official
web page https://go.spbu.ru/20a2711 .
| [
{
"created": "Sat, 28 Nov 2020 12:12:51 GMT",
"version": "v1"
}
] | 2020-12-01 | [
[
"Ievlev",
"E.",
""
]
] | This thesis is devoted to studying strong coupling phenomena (and confinement in particular) in supersymmetric gauge theories. The central object of investigation is the non-Abelian string that is responsible for the "instead-of-confinement" phase for monopoles in 4D ${\mathcal N} = 2$ supersymmetric QCD with the U($N$) gauge group and $N_f$ flavors of quark hypermultiplets, $N \leqslant N_f \leqslant 2 N$. Here it is shown that the non-Abelian strings and confined monopoles survive when we transition to the ${\mathcal N} = 1$ supersymmetric QCD. To this end we consider a mass term $\mu$ for the adjoint matter, and in the limit of large $\mu$ the bulk theory flows to ${\mathcal N} = 1$. We consider this transition both from the bulk point of view and from the world sheet theory, which is the two-dimensional $\mathbb{CP}(N-1)$ model. Survival of monopoles in the ${\mathcal N} = 1$ supersymmetric QCD is important for the "instead-of-confinement" phase, and also for the Seiberg-Witten picture of confinement. Apart from that, we also consider non-Abelian vortex strings in 4D $\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has been recently shown that these vortices behave as critical superstrings. In particular, the lowest string state appears to be a massless BPS "baryon." Here we show the occurrence of this stringy baryon using a purely field-theoretic method. Moreover, we explicitly demonstrate the "instead-of-confinement" phase, when the screened quarks and gauge bosons of weak coupling are replaced by the confined monopole-antimonopole pairs of strong coupling. English version. Full text (Russian and English) is available at the official web page https://go.spbu.ru/20a2711 . |
hep-th/0212092 | Ishwaree P. Neupane | Ishwaree P. Neupane | Black hole entropy in string-generated gravity models | 5 pages, 3 figures, Physical Review D (Rapid Communication) version | Phys.Rev. D67 (2003) 061501 | 10.1103/PhysRevD.67.061501 | null | hep-th | null | The Euclidean action and entropy are computed in string-generated gravity
models with quadratic curvatures, and used to argue that a negative mass
extremal metric is the background for hyperbolic (k=-1) black hole spacetimes,
k being the curvature constant of the event horizon. The entropy associated
with a black hole is always positive for k=(0,1) family. The positivity of
energy condition also ensures that the k=-1 (extremal) entropy is non-negative.
| [
{
"created": "Mon, 9 Dec 2002 08:53:26 GMT",
"version": "v1"
},
{
"created": "Thu, 26 Dec 2002 08:47:29 GMT",
"version": "v2"
},
{
"created": "Mon, 17 Feb 2003 15:29:08 GMT",
"version": "v3"
}
] | 2009-11-07 | [
[
"Neupane",
"Ishwaree P.",
""
]
] | The Euclidean action and entropy are computed in string-generated gravity models with quadratic curvatures, and used to argue that a negative mass extremal metric is the background for hyperbolic (k=-1) black hole spacetimes, k being the curvature constant of the event horizon. The entropy associated with a black hole is always positive for k=(0,1) family. The positivity of energy condition also ensures that the k=-1 (extremal) entropy is non-negative. |
2210.02802 | Hong-Da Lyu | Yan Liu, Hong-Da Lyu and Jun-Kun Zhao | Properties of gapped systems in AdS/BCFT | 36 pages, 17 figures, published version | Phys.Rev.D 107 (2023) 6, 066017 | 10.1103/PhysRevD.107.066017 | null | hep-th cond-mat.str-el | http://creativecommons.org/licenses/by/4.0/ | We study the conductivities and entanglement structures of two different
holographic gapped systems at zero density in the presence of boundaries within
AdS/BCFT. The first gapped system is described by the Einstein-scalar gravity
and the second one is the dual of AdS soliton geometry. We show that in both
these two systems the bulk and boundary conductivities along the spatial
direction of the boundary of BCFT are trivial. For the first system, when we
increase the size of the subsystem the renormalized entanglement entropy is
always non-negative and monotonically decreasing with discontinuous, or
continuous, or smooth behavior, depending on the effective tension of the
brane. While for the AdS soliton with a boundary, the renormalized entanglement
entropy only exhibits a discontinuous drop when we increase the size of the
subsystem.
| [
{
"created": "Thu, 6 Oct 2022 10:27:32 GMT",
"version": "v1"
},
{
"created": "Fri, 24 Mar 2023 09:52:19 GMT",
"version": "v2"
}
] | 2023-03-27 | [
[
"Liu",
"Yan",
""
],
[
"Lyu",
"Hong-Da",
""
],
[
"Zhao",
"Jun-Kun",
""
]
] | We study the conductivities and entanglement structures of two different holographic gapped systems at zero density in the presence of boundaries within AdS/BCFT. The first gapped system is described by the Einstein-scalar gravity and the second one is the dual of AdS soliton geometry. We show that in both these two systems the bulk and boundary conductivities along the spatial direction of the boundary of BCFT are trivial. For the first system, when we increase the size of the subsystem the renormalized entanglement entropy is always non-negative and monotonically decreasing with discontinuous, or continuous, or smooth behavior, depending on the effective tension of the brane. While for the AdS soliton with a boundary, the renormalized entanglement entropy only exhibits a discontinuous drop when we increase the size of the subsystem. |
1407.1048 | Francisco Pedro | Michele Cicoli, Sean Downes, Bhaskar Dutta, Francisco G. Pedro and
Alexander Westphal | Just enough inflation: power spectrum modifications at large scales | 31 pages, 13 figures | null | 10.1088/1475-7516/2014/12/030 | DESY-14-117 | hep-th astro-ph.CO hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We show that models of `just enough' inflation, where the slow-roll evolution
lasted only $50-60$ e-foldings, feature modifications of the CMB power spectrum
at large angular scales. We perform a systematic and model-independent analysis
of any possible non-slow-roll background evolution prior to the final stage of
slow-roll inflation. We find a high degree of universality since most common
backgrounds like fast-roll evolution, matter or radiation-dominance give rise
to a power loss at large angular scales and a peak together with an oscillatory
behaviour at scales around the value of the Hubble parameter at the beginning
of slow-roll inflation. Depending on the value of the equation of state
parameter, different pre-inflationary epochs lead instead to an enhancement of
power at low-$\ell$, and so seem disfavoured by recent observational hints for
a lack of CMB power at $\ell\lesssim 40$. We also comment on the importance of
initial conditions and the possibility to have multiple pre-inflationary
stages.
| [
{
"created": "Thu, 3 Jul 2014 20:00:06 GMT",
"version": "v1"
}
] | 2015-06-22 | [
[
"Cicoli",
"Michele",
""
],
[
"Downes",
"Sean",
""
],
[
"Dutta",
"Bhaskar",
""
],
[
"Pedro",
"Francisco G.",
""
],
[
"Westphal",
"Alexander",
""
]
] | We show that models of `just enough' inflation, where the slow-roll evolution lasted only $50-60$ e-foldings, feature modifications of the CMB power spectrum at large angular scales. We perform a systematic and model-independent analysis of any possible non-slow-roll background evolution prior to the final stage of slow-roll inflation. We find a high degree of universality since most common backgrounds like fast-roll evolution, matter or radiation-dominance give rise to a power loss at large angular scales and a peak together with an oscillatory behaviour at scales around the value of the Hubble parameter at the beginning of slow-roll inflation. Depending on the value of the equation of state parameter, different pre-inflationary epochs lead instead to an enhancement of power at low-$\ell$, and so seem disfavoured by recent observational hints for a lack of CMB power at $\ell\lesssim 40$. We also comment on the importance of initial conditions and the possibility to have multiple pre-inflationary stages. |
2012.15780 | Jaroslav Trnka | Jaroslav Trnka | Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes | 72 pages, 50 figures | null | 10.1007/JHEP04(2021)253 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we present new expressions for n-point NMHV tree-level gravity
amplitudes. We introduce a method of factorization diagrams which is a simple
graphical representation of R-invariants in Yang-Mills theory. We define the
gravity analogues which we call G-invariants, and expand the NMHV gravity
amplitudes in terms of these objects. We provide explicit formulas of NMHV
gravity amplitudes up to eight points in terms of G-invariants, and give the
general definition for any number of points. We discuss the connection to BCFW
representation, special behavior under large momentum shift, the role of
momentum twistors and the intricate web of spurious poles cancelation. Because
of the close connection between R-invariants and the (tree-level) Amplituhedron
for Yang-Mills amplitudes, we speculate that the new expansion for gravity
amplitudes should correspond to the triangulation of the putative Gravituhedron
geometry.
| [
{
"created": "Thu, 31 Dec 2020 17:59:34 GMT",
"version": "v1"
}
] | 2021-05-12 | [
[
"Trnka",
"Jaroslav",
""
]
] | In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity analogues which we call G-invariants, and expand the NMHV gravity amplitudes in terms of these objects. We provide explicit formulas of NMHV gravity amplitudes up to eight points in terms of G-invariants, and give the general definition for any number of points. We discuss the connection to BCFW representation, special behavior under large momentum shift, the role of momentum twistors and the intricate web of spurious poles cancelation. Because of the close connection between R-invariants and the (tree-level) Amplituhedron for Yang-Mills amplitudes, we speculate that the new expansion for gravity amplitudes should correspond to the triangulation of the putative Gravituhedron geometry. |
2004.01391 | James Edwards Prof | Naser Ahmadiniaz, Victor Miguel Banda Guzman, Fiorenzo Bastianelli,
Olindo Corradini, James P. Edwards and Christian Schubert | Worldline master formulas for the dressed electron propagator, part 1:
Off-shell amplitudes | 50 pages, 4 figures | null | 10.1007/JHEP08(2020)018 | null | hep-th hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In the first-quantised worldline approach to quantum field theory, a
long-standing problem has been to extend this formalism to amplitudes involving
open fermion lines while maintaining the efficiency of the well-tested
closed-loop case. In the present series of papers, we develop a suitable
formalism for the case of quantum electrodynamics in vacuum (part one and two)
and in a constant external electromagnetic field (part three), based on
second-order fermions and the symbol map. We derive this formalism from
standard field theory, but also give an alternative derivation intrinsic to the
worldline theory. In this first part, we use it to obtain a Bern-Kosower type
master formula for the fermion propagator, dressed with $N$ photons, in terms
of the "$N$-photon kernel," where off-shell this kernel appears also in
"subleading" terms involving only $N-1$ of the $N$ photons. Although the
parameter integrals generated by the master formula are equivalent to the usual
Feynman diagrams, they are quite different since the use of the inverse symbol
map avoids the appearance of long products of Dirac matrices. As a test we use
the $N=2$ case for a recalculation of the one-loop fermion self energy, in $D$
dimensions and arbitrary covariant gauge, reproducing the known result. We find
that significant simplification can be achieved in this calculation choosing an
unusual momentum-dependent gauge parameter.
| [
{
"created": "Fri, 3 Apr 2020 06:14:12 GMT",
"version": "v1"
}
] | 2020-08-26 | [
[
"Ahmadiniaz",
"Naser",
""
],
[
"Guzman",
"Victor Miguel Banda",
""
],
[
"Bastianelli",
"Fiorenzo",
""
],
[
"Corradini",
"Olindo",
""
],
[
"Edwards",
"James P.",
""
],
[
"Schubert",
"Christian",
""
]
] | In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with $N$ photons, in terms of the "$N$-photon kernel," where off-shell this kernel appears also in "subleading" terms involving only $N-1$ of the $N$ photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the $N=2$ case for a recalculation of the one-loop fermion self energy, in $D$ dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation choosing an unusual momentum-dependent gauge parameter. |
hep-th/9312100 | Yasui Yukinori | Yukinori Yasui and Satoshi Takahashi | Unstable geodesics and topological field theory | 28 pages, OCU-151 | J.Math.Phys. 35 (1994) 4547-4567 | 10.1063/1.530803 | null | hep-th | null | A topological field theory is used to study the cohomology of mapping space.
The cohomology is identified with the BRST cohomology realizing the physical
Hilbert space and the coboundary operator given by the calculations of
tunneling between the perturbative vacua. Our method is illustrated by a simple
example.
| [
{
"created": "Mon, 13 Dec 1993 11:43:06 GMT",
"version": "v1"
}
] | 2009-10-22 | [
[
"Yasui",
"Yukinori",
""
],
[
"Takahashi",
"Satoshi",
""
]
] | A topological field theory is used to study the cohomology of mapping space. The cohomology is identified with the BRST cohomology realizing the physical Hilbert space and the coboundary operator given by the calculations of tunneling between the perturbative vacua. Our method is illustrated by a simple example. |
1905.09030 | Juan Mateos Guilarte | A. Alonso-Izquierdo, R. Fresneda, J. Mateos Guilarte, D. Vassilevich | Soliton Fermionic number from the heat kernel expansion | LaTex file, 20 pages, 1 Figure, One Reference added | null | null | null | hep-th math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider different methods of calculating the (fractional) fermion number
of solitons based on the heat kernel expansion. We derive a formula for the
localized eta function a more systematic version of the derivative expansion
for spectral assymmetry and that provides a more systematic version of the
derivative expansion for spectral asymmetry and compute the fermion number in a
multiflavour extension of the Goldstone-Wilczek model.We also propose an
improved expansionof the heat kernelthat allows the tackling ofthe convergence
issues and permits an automated computation of the coefficients
| [
{
"created": "Wed, 22 May 2019 09:11:24 GMT",
"version": "v1"
},
{
"created": "Mon, 27 May 2019 15:21:09 GMT",
"version": "v2"
}
] | 2019-05-28 | [
[
"Alonso-Izquierdo",
"A.",
""
],
[
"Fresneda",
"R.",
""
],
[
"Guilarte",
"J. Mateos",
""
],
[
"Vassilevich",
"D.",
""
]
] | We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized eta function a more systematic version of the derivative expansion for spectral assymmetry and that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multiflavour extension of the Goldstone-Wilczek model.We also propose an improved expansionof the heat kernelthat allows the tackling ofthe convergence issues and permits an automated computation of the coefficients |
1405.3959 | Toshifumi Noumi | Anupam Mazumdar, Toshifumi Noumi, Masahide Yamaguchi | Dynamical breaking of shift-symmetry in supergravity-based inflation | 8 pages, no figure; v2: minor revision, estimation of the inflaton
potential is corrected; v3: minor revision, published version, title is
changed | Phys. Rev. D 90, 043519 (2014) | 10.1103/PhysRevD.90.043519 | RIKEN-MP-89 | hep-th astro-ph.CO gr-qc hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Shift-symmetry is essential to protect the flatness of the potential, even
beyond the super-Planckian vacuum expectation value (VEV) for an inflaton
field. The breaking of the shift-symmetry can yield potentials suitable for
super-Planckian excursion of the inflaton. The aim of this paper is to
illustrate that it is indeed possible to break the shift-symmetry dynamically
within 4 dimensional supergravity prior to a long phase of inflation. Thanks to
the shift-symmetry, the leading contribu- tion to the inflaton potential is
free from the dangerous exponential factor even after its breaking, which is
the main obstacle to realizing the super-Planckian inflation in supergravity.
But, in our simple model, the resulting inflaton potential is a cosine type
potential rather than the power-law one and it is difficult to realize a
super-Planckian breaking scale unfortunately.
| [
{
"created": "Thu, 15 May 2014 19:31:10 GMT",
"version": "v1"
},
{
"created": "Tue, 24 Jun 2014 04:08:12 GMT",
"version": "v2"
},
{
"created": "Fri, 3 Oct 2014 08:10:23 GMT",
"version": "v3"
}
] | 2014-10-06 | [
[
"Mazumdar",
"Anupam",
""
],
[
"Noumi",
"Toshifumi",
""
],
[
"Yamaguchi",
"Masahide",
""
]
] | Shift-symmetry is essential to protect the flatness of the potential, even beyond the super-Planckian vacuum expectation value (VEV) for an inflaton field. The breaking of the shift-symmetry can yield potentials suitable for super-Planckian excursion of the inflaton. The aim of this paper is to illustrate that it is indeed possible to break the shift-symmetry dynamically within 4 dimensional supergravity prior to a long phase of inflation. Thanks to the shift-symmetry, the leading contribu- tion to the inflaton potential is free from the dangerous exponential factor even after its breaking, which is the main obstacle to realizing the super-Planckian inflation in supergravity. But, in our simple model, the resulting inflaton potential is a cosine type potential rather than the power-law one and it is difficult to realize a super-Planckian breaking scale unfortunately. |
hep-th/0101117 | Amit Ghosh | Olaf Dreyer, Amit Ghosh and Jacek Wisniewski | Black hole entropy calculations based on symmetries | 14 pages, Latex, CGPG-01/1-1 | Class.Quant.Grav. 18 (2001) 1929-1938 | 10.1088/0264-9381/18/10/308 | null | hep-th gr-qc | null | Symmetry based approaches to the black hole entropy problem have a number of
attractive features; in particular they are very general and do not depend on
the details of the quantization method. However we point out that, of the two
available approaches, one faces conceptual problems (also emphasized by
others), while the second contains certain technical flaws. We correct these
errors and, within the new, improved scheme, calculate the entropy of
3-dimensional black holes. We find that, while the new symmetry vector fields
are well-defined on the ``stretched horizon,'' and lead to well-defined
Hamiltonians satisfying the expected Lie algebra, they fail to admit a
well-defined limit to the horizon. This suggests that, although the formal
calculation can be carried out at the classical level, its real, conceptual
origin probably lies in the quantum theory.
| [
{
"created": "Wed, 17 Jan 2001 21:58:02 GMT",
"version": "v1"
}
] | 2009-11-07 | [
[
"Dreyer",
"Olaf",
""
],
[
"Ghosh",
"Amit",
""
],
[
"Wisniewski",
"Jacek",
""
]
] | Symmetry based approaches to the black hole entropy problem have a number of attractive features; in particular they are very general and do not depend on the details of the quantization method. However we point out that, of the two available approaches, one faces conceptual problems (also emphasized by others), while the second contains certain technical flaws. We correct these errors and, within the new, improved scheme, calculate the entropy of 3-dimensional black holes. We find that, while the new symmetry vector fields are well-defined on the ``stretched horizon,'' and lead to well-defined Hamiltonians satisfying the expected Lie algebra, they fail to admit a well-defined limit to the horizon. This suggests that, although the formal calculation can be carried out at the classical level, its real, conceptual origin probably lies in the quantum theory. |
0803.2946 | Mokhtar Hassaine | Mokhtar Hassaine and Cristian Martinez | Higher-dimensional charged black holes solutions with a nonlinear
electrodynamics source | 7 pages. Minor corrections and references added | Class.Quant.Grav.25:195023,2008 | 10.1088/0264-9381/25/19/195023 | CECS-PHY-06/25 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We obtain electrically charged black hole solutions of the Einstein equations
in arbitrary dimensions with a nonlinear electrodynamics source. The matter
source is deriving from a Lagrangian given by an arbitrary power of the Maxwell
invariant. The form of the general solution suggests a natural partition for
the different ranges of this power. For a particular range, we exhibit a class
of solutions whose behavior resemble to the standard Reissner-Nordstrom black
holes. There also exists a range for which the black hole solutions approach
asymptotically the Minkowski spacetime slower than the Schwarzschild spacetime.
We have also found a family of not asymptotically flat black hole solutions
with an asymptotic behavior growing slower than the Schwarzschild (anti) de
Sitter spacetime. In odd dimensions, there exists a critical value of the
exponent for which the metric involves a logarithmic dependence. This critical
value corresponds to the transition between the standard behavior and the
solution decaying to Minkowski slower than the Schwarzschild spacetime.
| [
{
"created": "Thu, 20 Mar 2008 09:19:29 GMT",
"version": "v1"
},
{
"created": "Thu, 21 Aug 2008 18:35:54 GMT",
"version": "v2"
}
] | 2008-11-26 | [
[
"Hassaine",
"Mokhtar",
""
],
[
"Martinez",
"Cristian",
""
]
] | We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is deriving from a Lagrangian given by an arbitrary power of the Maxwell invariant. The form of the general solution suggests a natural partition for the different ranges of this power. For a particular range, we exhibit a class of solutions whose behavior resemble to the standard Reissner-Nordstrom black holes. There also exists a range for which the black hole solutions approach asymptotically the Minkowski spacetime slower than the Schwarzschild spacetime. We have also found a family of not asymptotically flat black hole solutions with an asymptotic behavior growing slower than the Schwarzschild (anti) de Sitter spacetime. In odd dimensions, there exists a critical value of the exponent for which the metric involves a logarithmic dependence. This critical value corresponds to the transition between the standard behavior and the solution decaying to Minkowski slower than the Schwarzschild spacetime. |
hep-th/9810005 | Galliano Valent | Evgeny Ivanov, Galliano Valent | Harmonic Space Construction of the Quaternionic Taub-NUT metric | 20 pages, Latex2e, no figures, a minor change in the conclusion | Class.Quant.Grav. 16 (1999) 1039-1056 | 10.1088/0264-9381/16/3/030 | JINR E2-98-249, LPTHE 98-44 | hep-th gr-qc | null | We present details of the harmonic space construction of a quaternionic
extension of the four-dimensional Taub-NUT metric. As the main merit of the
harmonic space approach, the metric is obtained in an explicit form following a
generic set of rules. It exhibits $SU(2)\times U(1)$ isometry group and depends
on two parameters, Taub-NUT `mass' and the cosmological constant. We consider
several limiting cases of interest which correspond to special choices of the
involved parameters.
| [
{
"created": "Thu, 1 Oct 1998 12:42:04 GMT",
"version": "v1"
},
{
"created": "Wed, 7 Oct 1998 14:19:29 GMT",
"version": "v2"
}
] | 2009-10-31 | [
[
"Ivanov",
"Evgeny",
""
],
[
"Valent",
"Galliano",
""
]
] | We present details of the harmonic space construction of a quaternionic extension of the four-dimensional Taub-NUT metric. As the main merit of the harmonic space approach, the metric is obtained in an explicit form following a generic set of rules. It exhibits $SU(2)\times U(1)$ isometry group and depends on two parameters, Taub-NUT `mass' and the cosmological constant. We consider several limiting cases of interest which correspond to special choices of the involved parameters. |
hep-th/9806203 | Steven Corley | S. Corley and T. Jacobson | Black hole lasers | RevTex, 13 pages, 4 eps figures; minor corrections, final version to
be published in Phys. Rev. D | Phys. Rev. D 59, 124011 (1999) | 10.1103/PhysRevD.59.124011 | null | hep-th gr-qc | null | High frequency dispersion does not alter the low frequency spectrum of
Hawking radiation from a single black hole horizon, whether the dispersion
entails subluminal or superluminal group velocities. We show here that in the
presence of an inner horizon as well as an outer horizon the superluminal case
differs dramatically however. The negative energy partners of Hawking quanta
return to the outer horizon and stimulate more Hawking radiation if the field
is bosonic or suppress it if the field is fermionic. This process leads to
exponential growth or damping of the radiated flux and correlations among the
quanta emitted at different times, unlike in the usual Hawking effect. These
phenomena may be observable in condensed matter black hole analogs that exhibit
"superluminal" dispersion.
| [
{
"created": "Wed, 24 Jun 1998 17:57:12 GMT",
"version": "v1"
},
{
"created": "Wed, 16 Dec 1998 18:16:17 GMT",
"version": "v2"
},
{
"created": "Mon, 15 Feb 1999 21:41:50 GMT",
"version": "v3"
}
] | 2016-08-25 | [
[
"Corley",
"S.",
""
],
[
"Jacobson",
"T.",
""
]
] | High frequency dispersion does not alter the low frequency spectrum of Hawking radiation from a single black hole horizon, whether the dispersion entails subluminal or superluminal group velocities. We show here that in the presence of an inner horizon as well as an outer horizon the superluminal case differs dramatically however. The negative energy partners of Hawking quanta return to the outer horizon and stimulate more Hawking radiation if the field is bosonic or suppress it if the field is fermionic. This process leads to exponential growth or damping of the radiated flux and correlations among the quanta emitted at different times, unlike in the usual Hawking effect. These phenomena may be observable in condensed matter black hole analogs that exhibit "superluminal" dispersion. |
1302.0798 | Stefano Bellucci | Stefano Bellucci and Vahagn Yeghikyan | The Coulomb problem on a 3-sphere and Heun polynomials | 8 pages, PACS 03.65.-w, 02.30.Ik, 14.80.Hv; typo in eqs. (9) and (12)
corrected | null | 10.1063/1.4817487 | null | hep-th math-ph math.MP quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We
present a special parametrization of the ellipto-spheroidal coordinate system
suitable for the separation of variables. After quantization we get the
explicit form of the spectrum and present an algebraic equation for the
eigenvalues of the Runge-Lentz vector. We also present the wave functions
expressed via Heun polynomials.
| [
{
"created": "Mon, 4 Feb 2013 18:53:17 GMT",
"version": "v1"
},
{
"created": "Tue, 5 Feb 2013 17:07:51 GMT",
"version": "v2"
},
{
"created": "Mon, 11 Feb 2013 09:39:48 GMT",
"version": "v3"
}
] | 2015-06-12 | [
[
"Bellucci",
"Stefano",
""
],
[
"Yeghikyan",
"Vahagn",
""
]
] | The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form of the spectrum and present an algebraic equation for the eigenvalues of the Runge-Lentz vector. We also present the wave functions expressed via Heun polynomials. |
1507.07434 | Kofinas Georgios | Georgios Kofinas | Hyperscaling violating black holes in scalar-torsion theories | Version to appear in Phys. Rev. D | Phys. Rev. D 92, 084022 (2015) | 10.1103/PhysRevD.92.084022 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study a gravity theory where a scalar field with potential, beyond its
minimal coupling, is also coupled through a non-minimal derivative coupling
with the torsion scalar which is the teleparallel equivalent of Einstein
gravity. This theory provides second order equations of motion and we find
large-distance non-perturbative static spherically symmetric four-dimensional
solutions. Among them a general class of black hole solutions is found for some
range of the parameters/integration constants with asymptotics of the form of
hyperscaling violating Lifshitz spacetime with spherical horizon topology.
Although the scalar field diverges at the horizon, its energy density and
pressures are finite there. From the astrophysical point of view, this solution
provides extra deflection of light compared to the Newtonian deflection.
| [
{
"created": "Mon, 27 Jul 2015 15:02:58 GMT",
"version": "v1"
},
{
"created": "Wed, 16 Sep 2015 20:33:44 GMT",
"version": "v2"
}
] | 2015-10-14 | [
[
"Kofinas",
"Georgios",
""
]
] | We study a gravity theory where a scalar field with potential, beyond its minimal coupling, is also coupled through a non-minimal derivative coupling with the torsion scalar which is the teleparallel equivalent of Einstein gravity. This theory provides second order equations of motion and we find large-distance non-perturbative static spherically symmetric four-dimensional solutions. Among them a general class of black hole solutions is found for some range of the parameters/integration constants with asymptotics of the form of hyperscaling violating Lifshitz spacetime with spherical horizon topology. Although the scalar field diverges at the horizon, its energy density and pressures are finite there. From the astrophysical point of view, this solution provides extra deflection of light compared to the Newtonian deflection. |
2202.09837 | Michele Santagata | J. M. Drummond, R. Glew, M. Santagata | BCJ relations in ${AdS}_5 \times S^3$ and the double-trace spectrum of
super gluons | 9 pages | null | 10.1103/PhysRevD.107.L081901 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We revisit the four-point function of super gluons in $AdS_5 \times S^3$ in
the spirit of the large $p$ formalism and show how the integrand of a
generalised Mellin transform satisfies various non-trivial properties such as
$U(1)$ decoupling identity, BCJ relations and colour-kinematic duality, in a
way that directly mirrors the analogous relations in flat space. We unmix the
spectrum of double-trace operators at large $N$ and find all anomalous
dimensions at leading order. The anomalous dimensions follow a very simple
pattern, resembling those of other theories with hidden conformal symmetries.
| [
{
"created": "Sun, 20 Feb 2022 15:30:44 GMT",
"version": "v1"
}
] | 2023-04-19 | [
[
"Drummond",
"J. M.",
""
],
[
"Glew",
"R.",
""
],
[
"Santagata",
"M.",
""
]
] | We revisit the four-point function of super gluons in $AdS_5 \times S^3$ in the spirit of the large $p$ formalism and show how the integrand of a generalised Mellin transform satisfies various non-trivial properties such as $U(1)$ decoupling identity, BCJ relations and colour-kinematic duality, in a way that directly mirrors the analogous relations in flat space. We unmix the spectrum of double-trace operators at large $N$ and find all anomalous dimensions at leading order. The anomalous dimensions follow a very simple pattern, resembling those of other theories with hidden conformal symmetries. |
hep-th/9305001 | Lev Vaidman | Yakir Aharonov and Lev Vaidman | The Schrodinger Wave is Observable after All! | 8, TAUP 2020-93# | null | null | null | hep-th | null | It is shown that it is possible to measure the Schr\"odinger wave of a single
quantum system. This provides a strong argument for associating physical
reality with a quantum state of a single system in sharp contrast with the
usual approach in which the physical meaning of a quantum state is related only
to an ensemble of identical systems. An apparent paradox between measurability
of a quantum state of a single system and the relativistic causality is
resolved.
| [
{
"created": "Mon, 3 May 1993 07:19:48 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Aharonov",
"Yakir",
""
],
[
"Vaidman",
"Lev",
""
]
] | It is shown that it is possible to measure the Schr\"odinger wave of a single quantum system. This provides a strong argument for associating physical reality with a quantum state of a single system in sharp contrast with the usual approach in which the physical meaning of a quantum state is related only to an ensemble of identical systems. An apparent paradox between measurability of a quantum state of a single system and the relativistic causality is resolved. |
2007.03693 | Timothy Cohen | Timothy Cohen and Daniel Green | Soft de Sitter Effective Theory | 51 pages + appendix + references, 31 footnotes | null | 10.1007/JHEP12(2020)041 | null | hep-th astro-ph.CO gr-qc hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Calculating the quantum evolution of a de Sitter universe on superhorizon
scales is notoriously difficult. To address this challenge, we introduce the
Soft de Sitter Effective Theory (SdSET). This framework holds for superhorizon
modes whose comoving momentum is far below the UV scale, which is set by the
inverse comoving horizon. The SdSET is formulated using the same approach that
yields the Heavy Quark Effective Theory. The degrees of freedom that capture
the long wavelength dynamics are identified with the growing and decaying
solutions to the equations of motion. The operator expansion is organized using
a power counting scheme, and loops can be regulated while respecting the low
energy symmetries. For massive quantum fields in a fixed de Sitter background,
power counting implies that all interactions beyond the horizon are irrelevant.
Alternatively, if the fields are very light, the leading interactions are at
most marginal, and resumming the associated logarithms using (dynamical)
renormalization group techniques yields the evolution equation for canonical
stochastic inflation. The SdSET is also applicable to models where gravity is
dynamical, including inflation. In this case, diffeomorphism invariance ensures
that all interactions are irrelevant, trivially implying the all-orders
conservation of adiabatic density fluctuations and gravitational waves. We
briefly touch on the application to slow-roll eternal inflation by identifying
novel relevant operators. This work serves to demystify many aspects of
perturbation theory outside the horizon, and has a variety of applications to
problems of cosmological interest.
| [
{
"created": "Tue, 7 Jul 2020 18:00:02 GMT",
"version": "v1"
}
] | 2020-12-30 | [
[
"Cohen",
"Timothy",
""
],
[
"Green",
"Daniel",
""
]
] | Calculating the quantum evolution of a de Sitter universe on superhorizon scales is notoriously difficult. To address this challenge, we introduce the Soft de Sitter Effective Theory (SdSET). This framework holds for superhorizon modes whose comoving momentum is far below the UV scale, which is set by the inverse comoving horizon. The SdSET is formulated using the same approach that yields the Heavy Quark Effective Theory. The degrees of freedom that capture the long wavelength dynamics are identified with the growing and decaying solutions to the equations of motion. The operator expansion is organized using a power counting scheme, and loops can be regulated while respecting the low energy symmetries. For massive quantum fields in a fixed de Sitter background, power counting implies that all interactions beyond the horizon are irrelevant. Alternatively, if the fields are very light, the leading interactions are at most marginal, and resumming the associated logarithms using (dynamical) renormalization group techniques yields the evolution equation for canonical stochastic inflation. The SdSET is also applicable to models where gravity is dynamical, including inflation. In this case, diffeomorphism invariance ensures that all interactions are irrelevant, trivially implying the all-orders conservation of adiabatic density fluctuations and gravitational waves. We briefly touch on the application to slow-roll eternal inflation by identifying novel relevant operators. This work serves to demystify many aspects of perturbation theory outside the horizon, and has a variety of applications to problems of cosmological interest. |
1508.01536 | Alfredo Herrera-Aguilar | A. Herrera-Aguilar and J.E. Paschalis | Towards the quantization of the non-relativistic D2-brane in the Pure
Spinor Formalism | 23 pages in latex, no figures; discussion added, some typos
corrected, more references added | null | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | An attempt is made to apply the pure spinor formalism to the non-relativistic
IIA D2-brane. The fermionic constraints corresponding to the rescaled fermionic
coordinates are given. Two commuting spinor fields are introduced, each one
corresponding to a fermionic constraint. A BRST charge is constructed via the
ansatz proposed by N. Berkovits. The nilpotency of the BRST charge leads to a
set of constraints for the two spinor fields including pure spinor constraints.
A novel non-trivial solution is given for one of the spinor fields which can be
written as a sum of two pure spinors.
| [
{
"created": "Thu, 6 Aug 2015 20:35:12 GMT",
"version": "v1"
},
{
"created": "Wed, 9 Sep 2015 02:45:45 GMT",
"version": "v2"
},
{
"created": "Wed, 5 Jun 2019 17:11:00 GMT",
"version": "v3"
}
] | 2019-06-06 | [
[
"Herrera-Aguilar",
"A.",
""
],
[
"Paschalis",
"J. E.",
""
]
] | An attempt is made to apply the pure spinor formalism to the non-relativistic IIA D2-brane. The fermionic constraints corresponding to the rescaled fermionic coordinates are given. Two commuting spinor fields are introduced, each one corresponding to a fermionic constraint. A BRST charge is constructed via the ansatz proposed by N. Berkovits. The nilpotency of the BRST charge leads to a set of constraints for the two spinor fields including pure spinor constraints. A novel non-trivial solution is given for one of the spinor fields which can be written as a sum of two pure spinors. |
hep-th/9808088 | null | R. Kallosh and A.A. Tseytlin | Simplifying superstring action on AdS_5 x S^5 | 15 pages, latex. Minor changes, references added | JHEP 9810:016,1998 | 10.1088/1126-6708/1998/10/016 | SU-ITP-98/49, Imperial/TP/97-98/65 | hep-th | null | Type IIB string action on AdS_5 x S^5 constructed in hep-th/9805028 is put
into a form where it becomes quadratic in fermions. This is achieved by
performing 2-d duality (T-duality) on the action in which kappa-symmetry was
fixed in the Killing gauge in hep-th/9808038. We discuss some properties and
possible applications of the resulting action.
| [
{
"created": "Fri, 14 Aug 1998 19:36:00 GMT",
"version": "v1"
},
{
"created": "Sun, 16 Aug 1998 18:09:51 GMT",
"version": "v2"
},
{
"created": "Thu, 27 Aug 1998 11:39:27 GMT",
"version": "v3"
}
] | 2009-10-31 | [
[
"Kallosh",
"R.",
""
],
[
"Tseytlin",
"A. A.",
""
]
] | Type IIB string action on AdS_5 x S^5 constructed in hep-th/9805028 is put into a form where it becomes quadratic in fermions. This is achieved by performing 2-d duality (T-duality) on the action in which kappa-symmetry was fixed in the Killing gauge in hep-th/9808038. We discuss some properties and possible applications of the resulting action. |
1702.00038 | Philip Phillips | Gabriele La Nave and Philip Phillips | Exact Form of Boundary Operators Dual to Interacting Bulk Scalar Fields
in the AdS/CFT Correspondence | The new submission has an extended discussion of the
Caffarelli/Silvestre extension theorem and its application to the AdS/CFT
correspondence | null | null | null | hep-th cond-mat.str-el math.DG | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Using holographic renormalization coupled with the
Caffarelli/Silvestre\cite{caffarelli} extension theorem, we calculate the
precise form of the boundary operator dual to a bulk scalar field rather than
just its average value. We show that even in the presence of interactions in
the bulk, the boundary operator dual to a bulk scalar field is an anti-local
operator, namely the fractional Laplacian. The propagator associated with such
operators is of the general power-law (fixed by the dimension of the scalar
field) type indicative of the absence of particle-like excitations at the
Wilson-Fisher fixed point or the phenomenological unparticle construction.
Holographic renormalization also allows us to show how radial quantization can
be extended to such non-local conformal operators.
| [
{
"created": "Tue, 31 Jan 2017 20:00:46 GMT",
"version": "v1"
},
{
"created": "Thu, 20 Apr 2017 23:00:05 GMT",
"version": "v2"
}
] | 2017-04-24 | [
[
"La Nave",
"Gabriele",
""
],
[
"Phillips",
"Philip",
""
]
] | Using holographic renormalization coupled with the Caffarelli/Silvestre\cite{caffarelli} extension theorem, we calculate the precise form of the boundary operator dual to a bulk scalar field rather than just its average value. We show that even in the presence of interactions in the bulk, the boundary operator dual to a bulk scalar field is an anti-local operator, namely the fractional Laplacian. The propagator associated with such operators is of the general power-law (fixed by the dimension of the scalar field) type indicative of the absence of particle-like excitations at the Wilson-Fisher fixed point or the phenomenological unparticle construction. Holographic renormalization also allows us to show how radial quantization can be extended to such non-local conformal operators. |
1408.2459 | Song He | Yuntao Bai, Song He | The Amplituhedron from Momentum Twistor Diagrams | 39 pages, 34 figures | null | 10.1007/JHEP02(2015)065 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We propose a new diagrammatic formulation of the all-loop scattering
amplitudes/Wilson loops in planar N=4 SYM, dubbed the "momentum-twistor
diagrams". These are on-shell-diagrams obtained by gluing trivalent black and
white vertices defined in momentum twistor space, which, in the reduced diagram
case, are known to be related to diagrams in the original twistor space. The
new diagrams are manifestly Yangian invariant, and they naturally represent
factorization and forward-limit contributions in the all-loop BCFW recursion
relations in momentum twistor space, in a fashion that is completely different
from those in momentum space. We show how to construct and evaluate
momentum-twistor diagrams, and how to use them to obtain tree-level amplitudes
and loop-level integrands; in particular for the latter we identify an isolated
bubble-structure for each loop variable, arising from a forward limit, or
entangled removal of particles. From a given diagram one can directly read off
the C, D matrices via a generalized "boundary measurement"; this in turn
determines a cell in the amplituhedron associated with the amplitude, and our
diagrammatic representations of the amplitude can provide triangulations of the
amplituhedron with generally very intricate geometries. To demonstrate the
computational power of the formalism, we give explicit results for general
two-loop integrands, and the cells of the complete amplituhedron for two-loop
MHV amplitudes.
| [
{
"created": "Mon, 11 Aug 2014 16:18:04 GMT",
"version": "v1"
}
] | 2015-06-22 | [
[
"Bai",
"Yuntao",
""
],
[
"He",
"Song",
""
]
] | We propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N=4 SYM, dubbed the "momentum-twistor diagrams". These are on-shell-diagrams obtained by gluing trivalent black and white vertices defined in momentum twistor space, which, in the reduced diagram case, are known to be related to diagrams in the original twistor space. The new diagrams are manifestly Yangian invariant, and they naturally represent factorization and forward-limit contributions in the all-loop BCFW recursion relations in momentum twistor space, in a fashion that is completely different from those in momentum space. We show how to construct and evaluate momentum-twistor diagrams, and how to use them to obtain tree-level amplitudes and loop-level integrands; in particular for the latter we identify an isolated bubble-structure for each loop variable, arising from a forward limit, or entangled removal of particles. From a given diagram one can directly read off the C, D matrices via a generalized "boundary measurement"; this in turn determines a cell in the amplituhedron associated with the amplitude, and our diagrammatic representations of the amplitude can provide triangulations of the amplituhedron with generally very intricate geometries. To demonstrate the computational power of the formalism, we give explicit results for general two-loop integrands, and the cells of the complete amplituhedron for two-loop MHV amplitudes. |
1401.8063 | Urjit A. Yajnik | Urjit A. Yajnik, Sasmita Mishra, Debasish Borah | Spontaneous parity breaking with broken supersymmetry : cosmological
constraint | to appear in the proceedings of The 10th International Symposium on
Cosmology and Particle Astrophysics (CosPA2013). Covers some of the material
included in the proceedings of Eleventh Conference on the Intersections of
Particle and Nuclear Physics, (CIPANP 2012) | null | null | IITB-PHY-TH-1401 | hep-th hep-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Unified models incorporating the right handed neutrino in a symmetric way
generically possess parity symmetry. If this is broken spontaneously it results
in the formation of domain walls in the early Universe, whose persistence is
unwanted. A generic mechanism for destabilisation of such walls is a small
pressure difference signalled by difference in the free energy across the
walls. It is interesting to explore the possibility of such effects in
conjunction with the effects that break supersymmetry in a phenomenologically
acceptable way. Realising this possibility in the context of several scenarios
of supersymmetry breaking results in an upper bound on the scale of spontaneous
parity breaking, often much lower than the GUT scale. In the left-right
symmetric models studied, the upper bound is no higher than $10^{11}$GeV but a
scale as low as $10^5$GeV is acceptable.
| [
{
"created": "Fri, 31 Jan 2014 05:14:36 GMT",
"version": "v1"
}
] | 2014-02-03 | [
[
"Yajnik",
"Urjit A.",
""
],
[
"Mishra",
"Sasmita",
""
],
[
"Borah",
"Debasish",
""
]
] | Unified models incorporating the right handed neutrino in a symmetric way generically possess parity symmetry. If this is broken spontaneously it results in the formation of domain walls in the early Universe, whose persistence is unwanted. A generic mechanism for destabilisation of such walls is a small pressure difference signalled by difference in the free energy across the walls. It is interesting to explore the possibility of such effects in conjunction with the effects that break supersymmetry in a phenomenologically acceptable way. Realising this possibility in the context of several scenarios of supersymmetry breaking results in an upper bound on the scale of spontaneous parity breaking, often much lower than the GUT scale. In the left-right symmetric models studied, the upper bound is no higher than $10^{11}$GeV but a scale as low as $10^5$GeV is acceptable. |
1908.11347 | Jorge Russo | G. Arias-Tamargo, D. Rodriguez-Gomez and J.G. Russo | The large charge limit of scalar field theories and the Wilson-Fisher
fixed point at $\epsilon=0$ | 14 pages | null | 10.1007/JHEP10(2019)201 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the sector of large charge operators $\phi^n$ ($\phi$ being the
complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in
$4-\epsilon$ dimensions that emerges when the coupling takes the critical value
$g\sim \epsilon$. We show that, in the limit $g\to 0$, when the theory naively
approaches the gaussian fixed point, the sector of operators with $n\to \infty
$ at fixed $g\,n^2\equiv \lambda$ remains non-trivial. Surprisingly, one can
compute the exact 2-point function and thereby the non-trivial anomalous
dimension of the operator $\phi^n$ by a full resummation of Feynman diagrams.
The same result can be reproduced from a saddle point approximation to the path
integral, which partly explains the existence of the limit. Finally, we extend
these results to the three-dimensional $O(2)$-symmetric theory with
$(\bar{\phi}\,\phi)^3$ potential.
| [
{
"created": "Thu, 29 Aug 2019 16:53:49 GMT",
"version": "v1"
},
{
"created": "Mon, 2 Sep 2019 15:09:40 GMT",
"version": "v2"
},
{
"created": "Wed, 30 Oct 2019 15:40:26 GMT",
"version": "v3"
}
] | 2020-01-08 | [
[
"Arias-Tamargo",
"G.",
""
],
[
"Rodriguez-Gomez",
"D.",
""
],
[
"Russo",
"J. G.",
""
]
] | We study the sector of large charge operators $\phi^n$ ($\phi$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-\epsilon$ dimensions that emerges when the coupling takes the critical value $g\sim \epsilon$. We show that, in the limit $g\to 0$, when the theory naively approaches the gaussian fixed point, the sector of operators with $n\to \infty $ at fixed $g\,n^2\equiv \lambda$ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator $\phi^n$ by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional $O(2)$-symmetric theory with $(\bar{\phi}\,\phi)^3$ potential. |
hep-th/0308204 | Boris Zupnik | B.M. Zupnik | N=4 Multiplets in N=3 Harmonic Superspace | Latex file, 16 pages | Theor.Math.Phys. 140 (2004) 1121-1134; Teor.Mat.Fiz. 140 (2004)
269-283 | 10.1023/B:TAMP.0000036542.47378.ba | null | hep-th | null | It is shown that the N=3 harmonic-superfield equations of motion are
invariant with respect to the 4-th supersymmetry. The SU(3) harmonics are also
used to analyze a more flexible form of superfield constraints for the Abelian
N=4 vector multiplet and its N=3 decomposition. An alternative unusual
representation of the N=4 supersymmetry is realized on infinite multiplets of
analytic superfields in the N=3 harmonic superspace. U(1) charges of
superfields in these multiplets are parametrized by an integer- valued
parameter which plays the role of the discrete coordinate. Each superfield term
of the N=3 Yang-Mills action has the infinite-dimensional N=4 generalization.
The gauge group of this model contains an infinite number of superfield
parameters.
| [
{
"created": "Fri, 29 Aug 2003 09:25:39 GMT",
"version": "v1"
}
] | 2009-11-10 | [
[
"Zupnik",
"B. M.",
""
]
] | It is shown that the N=3 harmonic-superfield equations of motion are invariant with respect to the 4-th supersymmetry. The SU(3) harmonics are also used to analyze a more flexible form of superfield constraints for the Abelian N=4 vector multiplet and its N=3 decomposition. An alternative unusual representation of the N=4 supersymmetry is realized on infinite multiplets of analytic superfields in the N=3 harmonic superspace. U(1) charges of superfields in these multiplets are parametrized by an integer- valued parameter which plays the role of the discrete coordinate. Each superfield term of the N=3 Yang-Mills action has the infinite-dimensional N=4 generalization. The gauge group of this model contains an infinite number of superfield parameters. |
1704.00321 | Christos Ragiadakos | C. N. Ragiadakos | Pseudo-Conformal Field Theory | null | null | null | null | hep-th gr-qc math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The fundamental structure of the 4-dimensional spacetime is assumed to be the
lorentzian CR-structure (LCR-structure), which contains two correlated
3-dimensional CR-structures. It is defined by explicit Frobenius integrable
relations characterized by "left" and "right" CP(3) points. This LCR-structure
is invariant under a very restrictive tetrad-Weyl symmetry, which permits a
unique special second order partial differential equation applied to a
Yang-Mills field, identified with the gluon field. A class of metrics with the
corresponding self-dual forms are defined. After partially fixing the
tetrad-Weyl symmetry, the electroweak connection is also defined, which is
directly related with the class of LCR-tetrads of the structure. The "free
electron" LCR-structure is identified, which has gravitational and electroweak
potentials (dressings) with fermionic gyromagnetic ratio g=2. The corresponding
massless "neutrino" LCR-structure is also found. These two solitonic
configurations constitute the first leptonic generation identified with the
Petrov type D LCR-structure. The muon and tau leptonic generations are
identified with the Petrov type II and I respectively. Using the electron
LCR-structure, I compute the corresponding quark having an additional gluonic
potential and providing the explication of the lepton-quark correspondence. The
standard model is implied via the causal Bogoliubov, Epstein-Glaser and Scharf
procedure viewed as a targeted harmonic analysis in the rigged Hilbert-Fock
space of precise Poincare representations of the computed geometric structures.
| [
{
"created": "Sun, 2 Apr 2017 16:08:03 GMT",
"version": "v1"
},
{
"created": "Sun, 27 Aug 2017 08:38:52 GMT",
"version": "v2"
},
{
"created": "Mon, 19 Feb 2024 05:16:24 GMT",
"version": "v3"
}
] | 2024-02-20 | [
[
"Ragiadakos",
"C. N.",
""
]
] | The fundamental structure of the 4-dimensional spacetime is assumed to be the lorentzian CR-structure (LCR-structure), which contains two correlated 3-dimensional CR-structures. It is defined by explicit Frobenius integrable relations characterized by "left" and "right" CP(3) points. This LCR-structure is invariant under a very restrictive tetrad-Weyl symmetry, which permits a unique special second order partial differential equation applied to a Yang-Mills field, identified with the gluon field. A class of metrics with the corresponding self-dual forms are defined. After partially fixing the tetrad-Weyl symmetry, the electroweak connection is also defined, which is directly related with the class of LCR-tetrads of the structure. The "free electron" LCR-structure is identified, which has gravitational and electroweak potentials (dressings) with fermionic gyromagnetic ratio g=2. The corresponding massless "neutrino" LCR-structure is also found. These two solitonic configurations constitute the first leptonic generation identified with the Petrov type D LCR-structure. The muon and tau leptonic generations are identified with the Petrov type II and I respectively. Using the electron LCR-structure, I compute the corresponding quark having an additional gluonic potential and providing the explication of the lepton-quark correspondence. The standard model is implied via the causal Bogoliubov, Epstein-Glaser and Scharf procedure viewed as a targeted harmonic analysis in the rigged Hilbert-Fock space of precise Poincare representations of the computed geometric structures. |
hep-th/9607109 | Mironov | A.Marshakov, A.Mironov and A.Morozov | WDVV-like equations in N=2 SUSY Yang-Mills Theory | 15 pages, LaTeX, no figures | Phys.Lett. B389 (1996) 43-52 | 10.1016/S0370-2693(96)01231-2 | ITEP/TH-22/96, FIAN/TD-10/96 | hep-th | null | The prepotential $F(a_i)$, defining the low-energy effective action of the
$SU(N)$ ${\cal N}=2$ SUSY Yang-Mills theories, satisfies an enlarged set of the
WDVV-like equations $F_iF_k^{-1}F_j = F_jF_k^{-1}F_i$ for any triple $i,j,k =
1,\ldots,N-1$, where matrix $F_i$ is equal to $(F_i)_{mn} = \partial^3
F/\partial a_i\partial a_m\partial a_n$. The same equations are actually true
for generic topological theories. In contrast to the conventional formulation,
when $k$ is restricted to $k=0$, in the proposed system there is no
distinguished ``first'' time-variable, and indices can be raised with the help
of any ``metric'' $\eta_{mn}^{(k)} = (F_k)_{mn}$, not obligatory flat. All the
equations (for all $i,j,k$) are true simultaneously. This result provides a new
parallel between the Seiberg-Witten theory of low-energy gauge models in $4d$
and topological theories.
| [
{
"created": "Sun, 14 Jul 1996 23:06:04 GMT",
"version": "v1"
}
] | 2009-10-30 | [
[
"Marshakov",
"A.",
""
],
[
"Mironov",
"A.",
""
],
[
"Morozov",
"A.",
""
]
] | The prepotential $F(a_i)$, defining the low-energy effective action of the $SU(N)$ ${\cal N}=2$ SUSY Yang-Mills theories, satisfies an enlarged set of the WDVV-like equations $F_iF_k^{-1}F_j = F_jF_k^{-1}F_i$ for any triple $i,j,k = 1,\ldots,N-1$, where matrix $F_i$ is equal to $(F_i)_{mn} = \partial^3 F/\partial a_i\partial a_m\partial a_n$. The same equations are actually true for generic topological theories. In contrast to the conventional formulation, when $k$ is restricted to $k=0$, in the proposed system there is no distinguished ``first'' time-variable, and indices can be raised with the help of any ``metric'' $\eta_{mn}^{(k)} = (F_k)_{mn}$, not obligatory flat. All the equations (for all $i,j,k$) are true simultaneously. This result provides a new parallel between the Seiberg-Witten theory of low-energy gauge models in $4d$ and topological theories. |
1501.00603 | Zaim Slimane | Slimane Zaim | Anisotropic universe space-time non-commutativity and scalar particle
creation in the presence of a constant electric field | 13 pages, No figures | ROm. Journ. Phys., Number 5-6, Volume 61,P.743-754, 2016 | null | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the effect of the non-commutativity on the creation of scalar
particles from vacuum in the anisotropic universe space-time. We derive the
deformed Klein-Gordon equation up to second order in the non-commutativity
parameter using the general modified field equation. Then the canonical method
based on Bogoliubov transformation is applied to calculate the probability of
particle creation in vacuum and the corresponding number density in the $k$
mode. We deduce that the non-commutative space-time introduces a new source of
particle creation.
| [
{
"created": "Sat, 3 Jan 2015 20:40:36 GMT",
"version": "v1"
}
] | 2016-09-06 | [
[
"Zaim",
"Slimane",
""
]
] | We study the effect of the non-commutativity on the creation of scalar particles from vacuum in the anisotropic universe space-time. We derive the deformed Klein-Gordon equation up to second order in the non-commutativity parameter using the general modified field equation. Then the canonical method based on Bogoliubov transformation is applied to calculate the probability of particle creation in vacuum and the corresponding number density in the $k$ mode. We deduce that the non-commutative space-time introduces a new source of particle creation. |
2106.03889 | Diptarka Das | Diptarka Das, Shouvik Datta | Higher spin wormholes from modular bootstrap | 31 pages, 2 figures, matches published version | JHEP 2021, 10 (2021) | 10.1007/JHEP10(2021)010 | CERN-TH-2021-085 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We investigate the connection between spacetime wormholes and ensemble
averaging in the context of higher spin AdS$_3$/CFT$_2$. Using techniques from
modular bootstrap combined with some holographic inputs, we evaluate the
partition function of a Euclidean wormhole in AdS$_3$ higher spin gravity. The
fixed spin sectors of the dual CFT$_2$ exhibit features that starkly go beyond
conventional random matrix ensembles: power-law ramps in the spectral form
factor and potentials with a double-well/crest underlying the level statistics.
| [
{
"created": "Mon, 7 Jun 2021 18:07:48 GMT",
"version": "v1"
},
{
"created": "Thu, 7 Oct 2021 01:41:30 GMT",
"version": "v2"
}
] | 2021-10-08 | [
[
"Das",
"Diptarka",
""
],
[
"Datta",
"Shouvik",
""
]
] | We investigate the connection between spacetime wormholes and ensemble averaging in the context of higher spin AdS$_3$/CFT$_2$. Using techniques from modular bootstrap combined with some holographic inputs, we evaluate the partition function of a Euclidean wormhole in AdS$_3$ higher spin gravity. The fixed spin sectors of the dual CFT$_2$ exhibit features that starkly go beyond conventional random matrix ensembles: power-law ramps in the spectral form factor and potentials with a double-well/crest underlying the level statistics. |
hep-th/9505063 | Ralf Kerschner | Ralf Kerschner | On quantum field theories with finitely many degrees of freedom | 22 pages, LateX | null | null | Tue-prep-05-95-04 | hep-th | null | The existence of inequivalent representations in quantum field theory with
{\it finitely} many degrees of freedom is shown. Their properties are
exemplified and analysed for concrete and simple models. In particular the
relations to Bogoliubov--Valatin quasi-particles, to thermo field dynamics, and
to $q$--deformed quantum theories are put foreward. The thermal properties of
the non-trivial vacuum are given and it is shown that the thermodynamic
equilibrium state is uniquely obtained by an irreversible vacuum dynamics.
Finally, the theory is applied to a realistic model: the BCS--theory of
superconductivity. An exact solution in order $O(N^{-1})$ for the full particle
number conserving BCS--Hamiltonian with particle number symmetric ground state
is given.
| [
{
"created": "Thu, 11 May 1995 07:28:59 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Kerschner",
"Ralf",
""
]
] | The existence of inequivalent representations in quantum field theory with {\it finitely} many degrees of freedom is shown. Their properties are exemplified and analysed for concrete and simple models. In particular the relations to Bogoliubov--Valatin quasi-particles, to thermo field dynamics, and to $q$--deformed quantum theories are put foreward. The thermal properties of the non-trivial vacuum are given and it is shown that the thermodynamic equilibrium state is uniquely obtained by an irreversible vacuum dynamics. Finally, the theory is applied to a realistic model: the BCS--theory of superconductivity. An exact solution in order $O(N^{-1})$ for the full particle number conserving BCS--Hamiltonian with particle number symmetric ground state is given. |
2109.05245 | Reiji Yoshioka | H. Itoyama, A. Mironov, A. Morozov, R. Yoshioka | Review on the Operator/Feynman diagram/Dessins d'enfant Correspondence
in Tensor Model | 11 pages, 5 figures | null | null | null | hep-th | http://creativecommons.org/licenses/by/4.0/ | A short review of the Operator/Feynman diagram/dessin d'enfants
correspondence in the rank 3 tensor model is presented, and the cut & join
operation is given in the language of dessin d'enfants as a straightforward
development. We classify operators of the rank 3 tensor model up to level 5
with dessin d'enfants.
| [
{
"created": "Sat, 11 Sep 2021 10:07:08 GMT",
"version": "v1"
}
] | 2021-09-14 | [
[
"Itoyama",
"H.",
""
],
[
"Mironov",
"A.",
""
],
[
"Morozov",
"A.",
""
],
[
"Yoshioka",
"R.",
""
]
] | A short review of the Operator/Feynman diagram/dessin d'enfants correspondence in the rank 3 tensor model is presented, and the cut & join operation is given in the language of dessin d'enfants as a straightforward development. We classify operators of the rank 3 tensor model up to level 5 with dessin d'enfants. |
2104.00052 | Timothy J. Hollowood | Timothy J. Hollowood, S. Prem Kumar, Andrea Legramandi and Neil Talwar | Islands in the Stream of Hawking Radiation | added clarifications and some minor corrections | null | 10.1007/JHEP11(2021)067 | null | hep-th gr-qc | http://creativecommons.org/licenses/by/4.0/ | We consider the island formula for the entropy of subsets of the Hawking
radiation in the adiabatic limit where the evaporation is very slow. We find a
simple concrete `on-shell' formula for the generalized entropy which involves
the image of the island out in the stream of radiation, the `island in the
stream'. The resulting recipe for the entropy allows us to calculate the
quantum information properties of the radiation and verify various constraints
including the Araki-Lieb inequality and strong subadditivity.
| [
{
"created": "Wed, 31 Mar 2021 18:21:11 GMT",
"version": "v1"
},
{
"created": "Mon, 26 Apr 2021 14:56:25 GMT",
"version": "v2"
},
{
"created": "Mon, 25 Oct 2021 07:42:20 GMT",
"version": "v3"
}
] | 2021-11-24 | [
[
"Hollowood",
"Timothy J.",
""
],
[
"Kumar",
"S. Prem",
""
],
[
"Legramandi",
"Andrea",
""
],
[
"Talwar",
"Neil",
""
]
] | We consider the island formula for the entropy of subsets of the Hawking radiation in the adiabatic limit where the evaporation is very slow. We find a simple concrete `on-shell' formula for the generalized entropy which involves the image of the island out in the stream of radiation, the `island in the stream'. The resulting recipe for the entropy allows us to calculate the quantum information properties of the radiation and verify various constraints including the Araki-Lieb inequality and strong subadditivity. |
hep-th/9906226 | Vijay Balasubramanian | Vijay Balasubramanian and Simon F. Ross | Holographic Particle Detection | 26 pages, LaTeX, 7 figures, uses epsf.sty | Phys.Rev. D61 (2000) 044007 | 10.1103/PhysRevD.61.044007 | HUTP-99/A032, UCSBTH-99-1 | hep-th | null | In anti-de Sitter (AdS) space, classical supergravity solutions are
represented "holographically" by conformal field theory (CFT) states in which
operators have expectation values. These 1-point functions are directly related
to the asymptotic behaviour of bulk fields. In some cases, distinct
supergravity solutions have identical asymptotic behaviour; so dual expectation
values are insufficient to distinguish them. We argue that non-local objects in
the gauge theory can resolve the ambiguity, and explicitly show that
collections of point particles in AdS_3 can be detected by studying kinks in
dual CFT Green functions. Three dimensional black holes can be formed by
collision of such particles. We show how black hole formation can be detected
in the holographic dual, and calculate CFT quantities that are sensitive to the
distribution of matter inside the event horizon.
| [
{
"created": "Tue, 29 Jun 1999 04:22:10 GMT",
"version": "v1"
}
] | 2009-10-31 | [
[
"Balasubramanian",
"Vijay",
""
],
[
"Ross",
"Simon F.",
""
]
] | In anti-de Sitter (AdS) space, classical supergravity solutions are represented "holographically" by conformal field theory (CFT) states in which operators have expectation values. These 1-point functions are directly related to the asymptotic behaviour of bulk fields. In some cases, distinct supergravity solutions have identical asymptotic behaviour; so dual expectation values are insufficient to distinguish them. We argue that non-local objects in the gauge theory can resolve the ambiguity, and explicitly show that collections of point particles in AdS_3 can be detected by studying kinks in dual CFT Green functions. Three dimensional black holes can be formed by collision of such particles. We show how black hole formation can be detected in the holographic dual, and calculate CFT quantities that are sensitive to the distribution of matter inside the event horizon. |
hep-th/9504053 | Jutta Kunz | Burkhard Kleihaus, Jutta Kunz and Abha Sood | SU(3) Einstein-Yang-Mills Sphalerons and Black Holes | LATEX, 16 pages, 5 figures | Phys.Lett. B354 (1995) 240-246 | 10.1016/0370-2693(95)00664-7 | THU-95/8 | hep-th gr-qc | null | In the SU(3) Einstein-Yang-Mills system sequences of static spherically
symmetric regular solutions and black hole solutions exist for both the SU(2)
and the SO(3) embedding. We construct the lowest regular solutions of the SO(3)
embedding, missed previously, and the corresponding black holes. The SO(3)
solutions are classified according to their boundary conditions and the number
of nodes of the matter functions. Both, the regular and the black hole
solutions are unstable.
| [
{
"created": "Mon, 10 Apr 1995 11:39:25 GMT",
"version": "v1"
}
] | 2009-10-28 | [
[
"Kleihaus",
"Burkhard",
""
],
[
"Kunz",
"Jutta",
""
],
[
"Sood",
"Abha",
""
]
] | In the SU(3) Einstein-Yang-Mills system sequences of static spherically symmetric regular solutions and black hole solutions exist for both the SU(2) and the SO(3) embedding. We construct the lowest regular solutions of the SO(3) embedding, missed previously, and the corresponding black holes. The SO(3) solutions are classified according to their boundary conditions and the number of nodes of the matter functions. Both, the regular and the black hole solutions are unstable. |
hep-th/0404223 | Anton Rebhan | Anton Rebhan, Peter van Nieuwenhuizen, Robert Wimmer | New developments in the quantization of supersymmetric solitons (kinks,
vortices and monopoles) | 15 pages, REVTEX4 style, 1 embedded postscript figure. Extended
writeup of a talk given by P. van Nieuwenhuizen at the XXIV Brazilian
National Meeting on Particles and Fields (Caxambu, Brazil, 30 Sep - 4 Oct
2003); to appear in the Brazilian Journal of Physics | Braz.J.Phys. 34 (2004) 1273-1287 | null | TUW-04-07, YITP-SB-04-10, ITP-UH-08/04 | hep-th | null | We discuss the one-loop quantum corrections to the mass M and central charge
Z of supersymmetric solitons: the kink, the vortex and the monopole. Contrary
to previous expectations and published results, in each of these cases there
are nonvanishing quantum corrections to the mass. For the N=1 kink and the N=2
monopole a new anomaly in Z rescues BPS saturation (M=Z); for the N=2 vortex,
BPS saturation is rescued for two reasons: (i) the quantum fluctuations of the
Higgs field acquire a nontrivial phase due to the winding of the classical
solution, and (ii) a fermionic zero mode used in the literature is shown not to
be normalizable.
| [
{
"created": "Wed, 28 Apr 2004 13:02:42 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Rebhan",
"Anton",
""
],
[
"van Nieuwenhuizen",
"Peter",
""
],
[
"Wimmer",
"Robert",
""
]
] | We discuss the one-loop quantum corrections to the mass M and central charge Z of supersymmetric solitons: the kink, the vortex and the monopole. Contrary to previous expectations and published results, in each of these cases there are nonvanishing quantum corrections to the mass. For the N=1 kink and the N=2 monopole a new anomaly in Z rescues BPS saturation (M=Z); for the N=2 vortex, BPS saturation is rescued for two reasons: (i) the quantum fluctuations of the Higgs field acquire a nontrivial phase due to the winding of the classical solution, and (ii) a fermionic zero mode used in the literature is shown not to be normalizable. |
1411.5641 | Ravikant Verma | Ravikant Verma | Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time | 15 | Eur.Phys.J.Plus 130 (2015) no.4, 79 | 10.1140/epjp/i2015-15079-3 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we investigate the twisted algebra of the fermionic
oscillators associated with Dirac field defined in $\kappa$-Minkowski
space-time. Starting from $\kappa$-deformed Dirac theory, which is invariant
under the undeformed $\kappa$-Poincare algebra, using the twisted flip
operator, we derive the deformed algebra of the creation and annihilation
operators corresponding to the Dirac field quanta in $\kappa$-Minkowski
space-time. In the limit $a\rightarrow 0$, the deformed algebra reduces to the
commutative result.
| [
{
"created": "Wed, 5 Nov 2014 04:17:48 GMT",
"version": "v1"
}
] | 2017-04-19 | [
[
"Verma",
"Ravikant",
""
]
] | In this paper, we investigate the twisted algebra of the fermionic oscillators associated with Dirac field defined in $\kappa$-Minkowski space-time. Starting from $\kappa$-deformed Dirac theory, which is invariant under the undeformed $\kappa$-Poincare algebra, using the twisted flip operator, we derive the deformed algebra of the creation and annihilation operators corresponding to the Dirac field quanta in $\kappa$-Minkowski space-time. In the limit $a\rightarrow 0$, the deformed algebra reduces to the commutative result. |
1412.1661 | Yurij Yaremko | Yurij Yaremko | Exact solution to the Landau-Lifshitz equation in a constant
electromagnetic field | null | J. Math. Phys., Vol. 54, 092901 (2013) | 10.1063/1.4820131 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We are interested in the motion of a classical charge acted upon an external
constant electromagnetic field where the back reaction of the particle's own
field is taken into account. The Landau-Lifshitz approximation to the
Lorentz-Abraham-Dirac equation is solved exactly and in closed form. It is
shown that the ultrarelativistic limit of the Landau-Lifshitz equation for a
radiating charge is the equation for eigenvalues and eigenvectors of the
external electromagnetic field tensor.
| [
{
"created": "Thu, 4 Dec 2014 13:30:17 GMT",
"version": "v1"
},
{
"created": "Tue, 2 May 2017 12:24:11 GMT",
"version": "v2"
}
] | 2017-05-03 | [
[
"Yaremko",
"Yurij",
""
]
] | We are interested in the motion of a classical charge acted upon an external constant electromagnetic field where the back reaction of the particle's own field is taken into account. The Landau-Lifshitz approximation to the Lorentz-Abraham-Dirac equation is solved exactly and in closed form. It is shown that the ultrarelativistic limit of the Landau-Lifshitz equation for a radiating charge is the equation for eigenvalues and eigenvectors of the external electromagnetic field tensor. |
2206.10626 | Alessia Benedetta Platania | Mathijs Fraaije, Alessia Platania, Frank Saueressig | On the reconstruction problem in Quantum Gravity | 12 pages (5 + appendices and bibliography), no figures | null | 10.1016/j.physletb.2022.137399 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Path integrals and the Wilsonian renormalization group provide two
complementary computational tools for investigating continuum approaches to
quantum gravity. The starting points of these constructions utilize a bare
action and a fixed point of the renormalization group flow, respectively. While
it is clear that there should be a connection between these ingredients, their
relation is far from trivial. This results in the so-called reconstruction
problem. In this work, we demonstrate that the map between these two
formulations does not generate non-localities at quadratic order in the
background curvature. At this level, the bare action in the path integral and
the fixed-point action obtained from the Wilsonian renormalization group differ
by local terms only. This conclusion does not apply to theories coming with a
physical ultraviolet cutoff or a fundamental non-locality scale.
| [
{
"created": "Tue, 21 Jun 2022 18:00:00 GMT",
"version": "v1"
}
] | 2022-08-31 | [
[
"Fraaije",
"Mathijs",
""
],
[
"Platania",
"Alessia",
""
],
[
"Saueressig",
"Frank",
""
]
] | Path integrals and the Wilsonian renormalization group provide two complementary computational tools for investigating continuum approaches to quantum gravity. The starting points of these constructions utilize a bare action and a fixed point of the renormalization group flow, respectively. While it is clear that there should be a connection between these ingredients, their relation is far from trivial. This results in the so-called reconstruction problem. In this work, we demonstrate that the map between these two formulations does not generate non-localities at quadratic order in the background curvature. At this level, the bare action in the path integral and the fixed-point action obtained from the Wilsonian renormalization group differ by local terms only. This conclusion does not apply to theories coming with a physical ultraviolet cutoff or a fundamental non-locality scale. |
hep-th/0508158 | Per Anders Sundell | E. Sezgin and P. Sundell | An Exact Solution of 4D Higher-Spin Gauge Theory | 47 pages. v3: global properties of the solution clarified, minor
corrections made, discussion and refs revised | Nucl.Phys. B762 (2007) 1-37 | 10.1016/j.nuclphysb.2006.06.038 | MIFP-05-18, UUITP-12/05 | hep-th | null | We give a one-parameter family of exact solutions to four-dimensional
higher-spin gauge theory invariant under a deformed higher-spin extension of
SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge
fields vanish, while the metric interpolates between two asymptotically AdS4
regions via a dS3-foliated domainwall and two H3-foliated Robertson-Walker
spacetimes -- one in the future and one in the past -- with the scalar field
playing the role of foliation parameter. All Weyl tensors vanish, including
that of spin two. We furthermore discuss methods for constructing solutions,
including deformation of solutions to pure AdS gravity, the gauge-function
approach, the perturbative treatment of (pseudo-)singular initial data
describing isometric or otherwise projected solutions, and zero-form
invariants.
| [
{
"created": "Mon, 22 Aug 2005 09:43:05 GMT",
"version": "v1"
},
{
"created": "Tue, 23 Aug 2005 11:34:22 GMT",
"version": "v2"
},
{
"created": "Sat, 31 Dec 2005 03:37:26 GMT",
"version": "v3"
}
] | 2010-04-05 | [
[
"Sezgin",
"E.",
""
],
[
"Sundell",
"P.",
""
]
] | We give a one-parameter family of exact solutions to four-dimensional higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS4 regions via a dS3-foliated domainwall and two H3-foliated Robertson-Walker spacetimes -- one in the future and one in the past -- with the scalar field playing the role of foliation parameter. All Weyl tensors vanish, including that of spin two. We furthermore discuss methods for constructing solutions, including deformation of solutions to pure AdS gravity, the gauge-function approach, the perturbative treatment of (pseudo-)singular initial data describing isometric or otherwise projected solutions, and zero-form invariants. |
0709.1199 | Hideki Maeda | Hideki Maeda and Masato Nozawa | Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet
gravity | 13 pages, no figures, 1 table; v4, new results added in the
asymptotically AdS case, accepted for publication in Physical Review D | Phys.Rev.D77:064031,2008 | 10.1103/PhysRevD.77.064031 | CECS-PHY-07/10 | hep-th gr-qc | null | We investigate properties of a quasi-local mass in a higher-dimensional
spacetime having symmetries corresponding to the isomertries of an
$(n-2)$-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity
in the presence of a cosmological constant. We assume that the Gauss-Bonnet
coupling constant is non-negative. The quasi-local mass was recently defined by
one of the authors as a counterpart of the Misner-Sharp quasi-local mass in
general relativity. The quasi-local mass is found to be a quasi-local conserved
charge associated with a locally conserved current constructed from the
generalized Kodama vector and exhibits the unified first law corresponding to
the energy-balance law. In the asymptotically flat case, it converges to the
Arnowitt-Deser-Misner mass at spacelike infinity, while it does to the
Deser-Tekin and Padilla mass at infinity in the case of asymptotically AdS.
Under the dominant energy condition, we show the monotonicity of the
quasi-local mass for any $k$, while the positivity on an untrapped hypersurface
with a regular center is shown for $k=1$ and for $k=0$ with an additional
condition, where $k=\pm1,0$ is the constant sectional curvature of each spatial
section of equipotential surfaces. Under a special relation between coupling
constants, positivity of the quasi-local mass is shown for any $k$ without
assumptions above. We also classify all the vacuum solutions by utilizing the
generalized Kodama vector. Lastly, several conjectures on further
generalization of the quasi-local mass in Lovelock gravity are proposed.
| [
{
"created": "Sat, 8 Sep 2007 10:50:13 GMT",
"version": "v1"
},
{
"created": "Wed, 12 Sep 2007 15:58:45 GMT",
"version": "v2"
},
{
"created": "Fri, 16 Nov 2007 19:35:21 GMT",
"version": "v3"
},
{
"created": "Wed, 20 Feb 2008 18:41:40 GMT",
"version": "v4"
}
] | 2008-11-26 | [
[
"Maeda",
"Hideki",
""
],
[
"Nozawa",
"Masato",
""
]
] | We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an $(n-2)$-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant. We assume that the Gauss-Bonnet coupling constant is non-negative. The quasi-local mass was recently defined by one of the authors as a counterpart of the Misner-Sharp quasi-local mass in general relativity. The quasi-local mass is found to be a quasi-local conserved charge associated with a locally conserved current constructed from the generalized Kodama vector and exhibits the unified first law corresponding to the energy-balance law. In the asymptotically flat case, it converges to the Arnowitt-Deser-Misner mass at spacelike infinity, while it does to the Deser-Tekin and Padilla mass at infinity in the case of asymptotically AdS. Under the dominant energy condition, we show the monotonicity of the quasi-local mass for any $k$, while the positivity on an untrapped hypersurface with a regular center is shown for $k=1$ and for $k=0$ with an additional condition, where $k=\pm1,0$ is the constant sectional curvature of each spatial section of equipotential surfaces. Under a special relation between coupling constants, positivity of the quasi-local mass is shown for any $k$ without assumptions above. We also classify all the vacuum solutions by utilizing the generalized Kodama vector. Lastly, several conjectures on further generalization of the quasi-local mass in Lovelock gravity are proposed. |
hep-th/9504019 | Simon Frederick Ross | S.W. Hawking and S.F. Ross | Duality between Electric and Magnetic Black Holes | 23 pages, revtex, no figures. Major revision: two sections on the
electric Ernst solution added | Phys.Rev.D52:5865-5876,1995 | 10.1103/PhysRevD.52.5865 | DAMTP/R-95/8 | hep-th gr-qc | null | A number of attempts have recently been made to extend the conjectured $S$
duality of Yang Mills theory to gravity. Central to these speculations has been
the belief that electrically and magnetically charged black holes, the solitons
of quantum gravity, have identical quantum properties. This is not obvious,
because although duality is a symmetry of the classical equations of motion, it
changes the sign of the Maxwell action. Nevertheless, we show that the chemical
potential and charge projection that one has to introduce for electric but not
magnetic black holes exactly compensate for the difference in action in the
semi-classical approximation. In particular, we show that the pair production
of electric black holes is not a runaway process, as one might think if one
just went by the action of the relevant instanton. We also comment on the
definition of the entropy in cosmological situations, and show that we need to
be more careful when defining the entropy than we are in an asymptotically-flat
case.
| [
{
"created": "Wed, 5 Apr 1995 18:00:24 GMT",
"version": "v1"
},
{
"created": "Wed, 17 May 1995 10:53:58 GMT",
"version": "v2"
}
] | 2008-11-26 | [
[
"Hawking",
"S. W.",
""
],
[
"Ross",
"S. F.",
""
]
] | A number of attempts have recently been made to extend the conjectured $S$ duality of Yang Mills theory to gravity. Central to these speculations has been the belief that electrically and magnetically charged black holes, the solitons of quantum gravity, have identical quantum properties. This is not obvious, because although duality is a symmetry of the classical equations of motion, it changes the sign of the Maxwell action. Nevertheless, we show that the chemical potential and charge projection that one has to introduce for electric but not magnetic black holes exactly compensate for the difference in action in the semi-classical approximation. In particular, we show that the pair production of electric black holes is not a runaway process, as one might think if one just went by the action of the relevant instanton. We also comment on the definition of the entropy in cosmological situations, and show that we need to be more careful when defining the entropy than we are in an asymptotically-flat case. |
hep-th/9510163 | Arut | G.E.Arutyunov | Construction of trigonometric Toda $r$-matrices via Hamiltonian
reduction of the cotangent bundle over loop groups | 10 pages, LATEX | null | null | null | hep-th | null | By applying the Hamiltonian reduction method to the cotangent bundle over
loop groups we recover the well-known classical trigonometric $r$-matrices of
the periodic Toda lattice.
| [
{
"created": "Mon, 23 Oct 1995 16:57:55 GMT",
"version": "v1"
},
{
"created": "Tue, 24 Oct 1995 15:39:53 GMT",
"version": "v2"
}
] | 2008-02-03 | [
[
"Arutyunov",
"G. E.",
""
]
] | By applying the Hamiltonian reduction method to the cotangent bundle over loop groups we recover the well-known classical trigonometric $r$-matrices of the periodic Toda lattice. |
0804.3839 | Hideo Kodama | Hideo Kodama | Accelerating a Black Hole in Higher Dimensions | 47 pages, 4 figures | Prog.Theor.Phys.120:371-411,2008 | 10.1143/PTP.120.371 | null | hep-th gr-qc | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Utilising the master equation with source for perturbations of the
Schwarzschild-Tangherlini solution, we construct perturbative solutions
representing a black hole accelerated by a string in higher dimensions. We show
that such solutions can be uniquely determined by a single function
representing the local tension of the string, under natural asymptotic and
regularity conditions. We further study whether we can construct a localised
braneworld black hole solution from such a solution by cutting off a region
containing the string by a hypersurface and putting a vacuum brane on the
boundary. We find that the solution corresponding to the string with constant
tension does not allow such brane configuration when the bulk spacetime
dimension is greater than four, in contrast to the four dimensional case.
Further, we show that there exist infinitely many localised braneworld black
hole solutions in the perturbative sense for four-dimensional bulk spacetime,
if we allow non-uniform string tensions.
| [
{
"created": "Thu, 24 Apr 2008 05:20:25 GMT",
"version": "v1"
}
] | 2009-01-25 | [
[
"Kodama",
"Hideo",
""
]
] | Utilising the master equation with source for perturbations of the Schwarzschild-Tangherlini solution, we construct perturbative solutions representing a black hole accelerated by a string in higher dimensions. We show that such solutions can be uniquely determined by a single function representing the local tension of the string, under natural asymptotic and regularity conditions. We further study whether we can construct a localised braneworld black hole solution from such a solution by cutting off a region containing the string by a hypersurface and putting a vacuum brane on the boundary. We find that the solution corresponding to the string with constant tension does not allow such brane configuration when the bulk spacetime dimension is greater than four, in contrast to the four dimensional case. Further, we show that there exist infinitely many localised braneworld black hole solutions in the perturbative sense for four-dimensional bulk spacetime, if we allow non-uniform string tensions. |
1801.04854 | Pietro Antonio Grassi | Roberto Catenacci and Pietro Antonio Grassi | String Sigma Models on Curved Supermanifolds | 18 pages. Contribution to the Special Issue of Universe "Super
Geometry for Super Strings" | null | null | ARC-18-01 | hep-th math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We use the techniques of integral forms to analyse the easiest example of two
dimensional sigma models on a supermanifold. We write the action as an integral
of a top integral form over a D=2 supermanifold and we show how to interpolate
between different superspace actions. Then, we consider curved supermanifolds
and we show that the definitions used for flat supermanifold can also be used
for curved supermanifolds. We prove it by first considering the case of a
curved rigid supermanifold and then the case of a generic curved supermanifold
described by a single superfield $E$.
| [
{
"created": "Mon, 15 Jan 2018 15:48:14 GMT",
"version": "v1"
}
] | 2018-01-16 | [
[
"Catenacci",
"Roberto",
""
],
[
"Grassi",
"Pietro Antonio",
""
]
] | We use the techniques of integral forms to analyse the easiest example of two dimensional sigma models on a supermanifold. We write the action as an integral of a top integral form over a D=2 supermanifold and we show how to interpolate between different superspace actions. Then, we consider curved supermanifolds and we show that the definitions used for flat supermanifold can also be used for curved supermanifolds. We prove it by first considering the case of a curved rigid supermanifold and then the case of a generic curved supermanifold described by a single superfield $E$. |
2107.00041 | Kausik Ghosh | Kausik Ghosh, Apratim Kaviraj, Miguel F. Paulos | Charging Up the Functional Bootstrap | 44 pages, 8 figures, typos corrected, minor details added, references
added | null | 10.1007/JHEP10(2021)116 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We revisit the problem of bootstrapping CFT correlators of charged fields.
After discussing in detail how bounds for uncharged fields can be recycled to
the charged case, we introduce two sets of analytic functional bases for
correlators on the line. The first, which we call "simple", is essentially a
direct sum of analytic functionals for the uncharged case. We use it to
establish very general bounds on the OPE density appearing in charged
correlators. The second basis is dual to generalized free fields and we explain
how it is related to a charged version of the Polyakov bootstrap. We apply
these functionals to map out the space of correlators and obtain new improved
bounds on the 3d Ising twist defect.
| [
{
"created": "Wed, 30 Jun 2021 18:03:29 GMT",
"version": "v1"
},
{
"created": "Mon, 12 Jul 2021 15:03:26 GMT",
"version": "v2"
}
] | 2021-11-03 | [
[
"Ghosh",
"Kausik",
""
],
[
"Kaviraj",
"Apratim",
""
],
[
"Paulos",
"Miguel F.",
""
]
] | We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on the line. The first, which we call "simple", is essentially a direct sum of analytic functionals for the uncharged case. We use it to establish very general bounds on the OPE density appearing in charged correlators. The second basis is dual to generalized free fields and we explain how it is related to a charged version of the Polyakov bootstrap. We apply these functionals to map out the space of correlators and obtain new improved bounds on the 3d Ising twist defect. |
1704.07890 | Jacques Distler | Oscar Chacaltana, Jacques Distler, Anderson Trimm and Yinan Zhu | Tinkertoys for the E7 Theory | Fixed one entry in table of interacting fixtures with an irregular
puncture | null | 10.1007/JHEP05(2018)031 | UTTG--03--17 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We classify the class $S$ theories of type $E_7$. These are four-dimensional
$\mathcal{N}=2$ superconformal field theories arising from the compactification
of the $E_7$ $(2,0)$ theory on a punctured Riemann surface, $C$. The
classification is given by listing all 3-punctured spheres ("fixtures"), and
connecting cylinders, which can arise in a pants-decomposition of $C$. We find
exactly 11,000 fixtures with three regular punctures, and an additional 48 with
one "irregular puncture" (in the sense used in our previous works). To organize
this large number of theories, we have created a web application at
https://golem.ph.utexas.edu/class-S/E7/ . Among these theories, we find 10 new
ones with a simple exceptional global symmetry group, as well as a new rank-2
SCFT and several new rank-3 SCFTs. As an application, we study the
strong-coupling limit of the $E_7$ gauge theory with 3 hypermultiplets in the
$56$. Using our results, we also verify recent conjectures that the $T^2$
compactification of certain $6d$ $(1,0)$ theories can alternatively be realized
in class $S$ as fixtures in the $E_7$ or $E_8$ theories.
| [
{
"created": "Tue, 25 Apr 2017 20:00:01 GMT",
"version": "v1"
},
{
"created": "Sun, 25 Feb 2018 23:46:19 GMT",
"version": "v2"
}
] | 2018-10-04 | [
[
"Chacaltana",
"Oscar",
""
],
[
"Distler",
"Jacques",
""
],
[
"Trimm",
"Anderson",
""
],
[
"Zhu",
"Yinan",
""
]
] | We classify the class $S$ theories of type $E_7$. These are four-dimensional $\mathcal{N}=2$ superconformal field theories arising from the compactification of the $E_7$ $(2,0)$ theory on a punctured Riemann surface, $C$. The classification is given by listing all 3-punctured spheres ("fixtures"), and connecting cylinders, which can arise in a pants-decomposition of $C$. We find exactly 11,000 fixtures with three regular punctures, and an additional 48 with one "irregular puncture" (in the sense used in our previous works). To organize this large number of theories, we have created a web application at https://golem.ph.utexas.edu/class-S/E7/ . Among these theories, we find 10 new ones with a simple exceptional global symmetry group, as well as a new rank-2 SCFT and several new rank-3 SCFTs. As an application, we study the strong-coupling limit of the $E_7$ gauge theory with 3 hypermultiplets in the $56$. Using our results, we also verify recent conjectures that the $T^2$ compactification of certain $6d$ $(1,0)$ theories can alternatively be realized in class $S$ as fixtures in the $E_7$ or $E_8$ theories. |
hep-th/9808062 | Mikhail Plyushchay | Jorge Gamboa, Mikhail Plyushchay and Jorge Zanelli | Three aspects of bosonized supersymmetry and linear differential field
equation with reflection | 18 pages, LaTeX, minor typos corrected, ref updated, to appear in
Nucl. Phys. B | Nucl.Phys. B543 (1999) 447-465 | 10.1016/S0550-3213(98)00832-3 | null | hep-th hep-ph math-ph math.MP nucl-th quant-ph | null | Recently it was observed by one of the authors that supersymmetric quantum
mechanics (SUSYQM) admits a formulation in terms of only one bosonic degree of
freedom. Such a construction, called the minimally bosonized SUSYQM, appeared
in the context of integrable systems and dynamical symmetries. We show that the
minimally bosonized SUSYQM can be obtained from Witten's SUSYQM by applying to
it a nonlocal unitary transformation with a subsequent reduction to one of the
eigenspaces of the total reflection operator. The transformation depends on the
parity operator, and the deformed Heisenberg algebra with reflection,
intimately related to parabosons and parafermions, emerges here in a natural
way. It is shown that the minimally bosonized SUSYQM can also be understood as
supersymmetric two-fermion system. With this interpretation, the bosonization
construction is generalized to the case of N=1 supersymmetry in 2 dimensions.
The same special unitary transformation diagonalises the Hamiltonian operator
of the 2D massive free Dirac theory. The resulting Hamiltonian is not a square
root like in the Foldy-Wouthuysen case, but is linear in spatial derivative.
Subsequent reduction to `up' or `down' field component gives rise to a linear
differential equation with reflection whose `square' is the massive
Klein-Gordon equation. In the massless limit this becomes the self-dual Weyl
equation. The linear differential equation with reflection admits
generalizations to higher dimensions and can be consistently coupled to gauge
fields. The bosonized SUSYQM can also be generated applying the nonlocal
unitary transformation to the Dirac field in the background of a nonlinear
scalar field in a kink configuration.
| [
{
"created": "Tue, 11 Aug 1998 21:51:01 GMT",
"version": "v1"
},
{
"created": "Mon, 30 Nov 1998 23:55:08 GMT",
"version": "v2"
}
] | 2009-10-31 | [
[
"Gamboa",
"Jorge",
""
],
[
"Plyushchay",
"Mikhail",
""
],
[
"Zanelli",
"Jorge",
""
]
] | Recently it was observed by one of the authors that supersymmetric quantum mechanics (SUSYQM) admits a formulation in terms of only one bosonic degree of freedom. Such a construction, called the minimally bosonized SUSYQM, appeared in the context of integrable systems and dynamical symmetries. We show that the minimally bosonized SUSYQM can be obtained from Witten's SUSYQM by applying to it a nonlocal unitary transformation with a subsequent reduction to one of the eigenspaces of the total reflection operator. The transformation depends on the parity operator, and the deformed Heisenberg algebra with reflection, intimately related to parabosons and parafermions, emerges here in a natural way. It is shown that the minimally bosonized SUSYQM can also be understood as supersymmetric two-fermion system. With this interpretation, the bosonization construction is generalized to the case of N=1 supersymmetry in 2 dimensions. The same special unitary transformation diagonalises the Hamiltonian operator of the 2D massive free Dirac theory. The resulting Hamiltonian is not a square root like in the Foldy-Wouthuysen case, but is linear in spatial derivative. Subsequent reduction to `up' or `down' field component gives rise to a linear differential equation with reflection whose `square' is the massive Klein-Gordon equation. In the massless limit this becomes the self-dual Weyl equation. The linear differential equation with reflection admits generalizations to higher dimensions and can be consistently coupled to gauge fields. The bosonized SUSYQM can also be generated applying the nonlocal unitary transformation to the Dirac field in the background of a nonlinear scalar field in a kink configuration. |
2308.06312 | Brandon Rayhaun | Leonardo Rastelli and Brandon C. Rayhaun | Rationality in Four Dimensions | 7 pages | null | null | null | hep-th math.NT math.QA | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | By leveraging the physics of the Higgs branch, we argue that the conformal
central charges $a$ and $c$ of an arbitrary 4d $N=2$ superconformal field
theory (SCFT) are rational numbers. Our proof of the rationality of $c$ is
conditioned on a well-supported conjecture about how the Higgs branch of an
SCFT is encoded in its protected chiral algebra. To establish the rationality
of $a$, we further rely on a widely-believed technical assumption on the
high-temperature limit of the superconformal index.
| [
{
"created": "Fri, 11 Aug 2023 18:00:00 GMT",
"version": "v1"
}
] | 2023-08-15 | [
[
"Rastelli",
"Leonardo",
""
],
[
"Rayhaun",
"Brandon C.",
""
]
] | By leveraging the physics of the Higgs branch, we argue that the conformal central charges $a$ and $c$ of an arbitrary 4d $N=2$ superconformal field theory (SCFT) are rational numbers. Our proof of the rationality of $c$ is conditioned on a well-supported conjecture about how the Higgs branch of an SCFT is encoded in its protected chiral algebra. To establish the rationality of $a$, we further rely on a widely-believed technical assumption on the high-temperature limit of the superconformal index. |
hep-th/0108037 | Christian Mercat | C. H. Otto Chui, Christian Mercat and Paul A. Pearce | Integrable Boundaries and Universal TBA Functional Equations | 30 pages, amsmath,amssymb,hyperref,mcite,svcon2e (included)
Introduction rewritten, typos fixed, layout changed | Prog.Math.Phys. 23 (2002) 391-413 | null | null | hep-th | null | We derive the fusion hierarchy of functional equations for critical A-D-E
lattice models related to, the sl(2) unitary minimal models, the parafermionic
models and the supersymmetric models of conformal field theory, and deduce the
related TBA functional equations. The derivation uses fusion projectors and
applies in the presence of all known integrable boundary conditions on the
torus and cylinder. The resulting TBA functional equations are_universal_ in
the sense that they depend only on the Coxeter number of the A-D-E graph and
are independent of the particular integrable boundary conditions. We conjecture
generally that TBA functional equations are universal for all integrable
lattice models associated with rational CFTs and their integrable
perturbations.
| [
{
"created": "Tue, 7 Aug 2001 13:49:43 GMT",
"version": "v1"
},
{
"created": "Wed, 8 Aug 2001 07:28:39 GMT",
"version": "v2"
},
{
"created": "Tue, 30 Oct 2001 06:02:00 GMT",
"version": "v3"
}
] | 2007-05-23 | [
[
"Chui",
"C. H. Otto",
""
],
[
"Mercat",
"Christian",
""
],
[
"Pearce",
"Paul A.",
""
]
] | We derive the fusion hierarchy of functional equations for critical A-D-E lattice models related to, the sl(2) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory, and deduce the related TBA functional equations. The derivation uses fusion projectors and applies in the presence of all known integrable boundary conditions on the torus and cylinder. The resulting TBA functional equations are_universal_ in the sense that they depend only on the Coxeter number of the A-D-E graph and are independent of the particular integrable boundary conditions. We conjecture generally that TBA functional equations are universal for all integrable lattice models associated with rational CFTs and their integrable perturbations. |
hep-th/0210094 | Odintsov Sergey | S.D. Odintsov | Brane New World and dS/CFT correspondence | 10 pages, based on plenary talk at GRG11, Tomsk, July 2002 | Grav.Cosmol.9:79-82,2003 | null | null | hep-th | null | The occurence of 5d de Sitter space with 4d de Sitter brane is discussed on
classical and quantum level. It is shown that quantum effects maybe produced by
dual CFT living on the brane. Moreover, gravity trapping on the brane is proved
via the presentation of 5d dS gravity as 4d gravity coupled with gauge theory.
This supports the dS/CFT correspondence. Some open questions in 5d dS/4d CFT
correspondence are briefly discussed.
| [
{
"created": "Thu, 10 Oct 2002 08:24:28 GMT",
"version": "v1"
}
] | 2009-09-17 | [
[
"Odintsov",
"S. D.",
""
]
] | The occurence of 5d de Sitter space with 4d de Sitter brane is discussed on classical and quantum level. It is shown that quantum effects maybe produced by dual CFT living on the brane. Moreover, gravity trapping on the brane is proved via the presentation of 5d dS gravity as 4d gravity coupled with gauge theory. This supports the dS/CFT correspondence. Some open questions in 5d dS/4d CFT correspondence are briefly discussed. |
1805.08782 | Sagar F. Lokhande | Alexandre Belin, Nabil Iqbal, Sagar F. Lokhande | Bulk entanglement entropy in perturbative excited states | 35 pages, 5 figures; v2 references added; v3: Typos corrected, as
requested by a SciPost Physics referee. The referee report can be found at
https://scipost.org/submission/1805.08782v2/ | SciPost Phys. 5, 024 (2018) | 10.21468/SciPostPhys.5.3.024 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We compute the bulk entanglement entropy across the Ryu-Takayanagi surface
for a one-particle state in a scalar field theory in AdS$_3$. We work directly
within the bulk Hilbert space and include the spatial spread of the scalar
wavefunction. We give closed form expressions in the limit of small interval
sizes and compare the result to a CFT computation of entanglement entropy in an
excited primary state at large $c$. Including the contribution from the
backreacted minimal area, we find agreement between the CFT result and the FLM
and JLMS formulas for quantum corrections to holographic entanglement entropy.
This provides a non-trivial check in a state where the answer is not dictated
by symmetry. Along the way, we provide closed-form expressions for the scalar
field Bogoliubov coefficients that relate the global and Rindler slicings of
AdS$_3$.
| [
{
"created": "Tue, 22 May 2018 18:00:01 GMT",
"version": "v1"
},
{
"created": "Wed, 27 Jun 2018 10:46:56 GMT",
"version": "v2"
},
{
"created": "Sun, 2 Sep 2018 08:44:16 GMT",
"version": "v3"
}
] | 2018-09-26 | [
[
"Belin",
"Alexandre",
""
],
[
"Iqbal",
"Nabil",
""
],
[
"Lokhande",
"Sagar F.",
""
]
] | We compute the bulk entanglement entropy across the Ryu-Takayanagi surface for a one-particle state in a scalar field theory in AdS$_3$. We work directly within the bulk Hilbert space and include the spatial spread of the scalar wavefunction. We give closed form expressions in the limit of small interval sizes and compare the result to a CFT computation of entanglement entropy in an excited primary state at large $c$. Including the contribution from the backreacted minimal area, we find agreement between the CFT result and the FLM and JLMS formulas for quantum corrections to holographic entanglement entropy. This provides a non-trivial check in a state where the answer is not dictated by symmetry. Along the way, we provide closed-form expressions for the scalar field Bogoliubov coefficients that relate the global and Rindler slicings of AdS$_3$. |
hep-th/0602097 | Ishwaree Neupane | Ishwaree P. Neupane | On compatibility of string effective action with an accelerating
universe | 30 pages, 8 figures; v2 significant changes in notations, appendix
and refs added; v3 significant revisions, refs added; v4 appendix extended,
new refs, published version | Class.Quant.Grav. 23 (2006) 7493-7520 | 10.1088/0264-9381/23/24/020 | null | hep-th astro-ph gr-qc | null | In this paper, we fully investigate the cosmological effects of the moduli
dependent one-loop corrections to the gravitational couplings of the string
effective action to explain the cosmic acceleration problem in early (and/or
late) universe. These corrections comprise a Gauss-Bonnet (GB) invariant
multiplied by universal non-trivial functions of the common modulus $\sigma$
and the dilaton $\phi$. The model exhibits several features of cosmological
interest, including the transition between deceleration and acceleration
phases. By considering some phenomenologically motivated ansatzs for one of the
scalars and/or the scale factor (of the universe), we also construct a number
of interesting inflationary potentials. In all examples under consideration, we
find that the model leads only to a standard inflation ($w \geq -1$) when the
numerical coefficient $\delta$ associated with modulus-GB coupling is positive,
while the model can lead also to a non-standard inflation ($w<-1$), if $\delta$
is negative. In the absence of (or trivial) coupling between the GB term and
the scalars, there is no crossing between the $w< -1$ and $w> -1$ phases, while
this is possible with non-trivial GB couplings, even for constant dilaton phase
of the standard picture. Within our model, after a sufficient amount of e-folds
of expansion, the rolling of both fields $\phi$ and $\sigma$ can be small. In
turn, any possible violation of equivalence principle or deviations from the
standard general relativity may be small enough to easily satisfy all
astrophysical and cosmological constraints.
| [
{
"created": "Fri, 10 Feb 2006 20:56:32 GMT",
"version": "v1"
},
{
"created": "Thu, 27 Apr 2006 11:01:02 GMT",
"version": "v2"
},
{
"created": "Wed, 26 Jul 2006 14:46:56 GMT",
"version": "v3"
},
{
"created": "Sun, 29 Oct 2006 22:02:48 GMT",
"version": "v4"
}
] | 2009-11-11 | [
[
"Neupane",
"Ishwaree P.",
""
]
] | In this paper, we fully investigate the cosmological effects of the moduli dependent one-loop corrections to the gravitational couplings of the string effective action to explain the cosmic acceleration problem in early (and/or late) universe. These corrections comprise a Gauss-Bonnet (GB) invariant multiplied by universal non-trivial functions of the common modulus $\sigma$ and the dilaton $\phi$. The model exhibits several features of cosmological interest, including the transition between deceleration and acceleration phases. By considering some phenomenologically motivated ansatzs for one of the scalars and/or the scale factor (of the universe), we also construct a number of interesting inflationary potentials. In all examples under consideration, we find that the model leads only to a standard inflation ($w \geq -1$) when the numerical coefficient $\delta$ associated with modulus-GB coupling is positive, while the model can lead also to a non-standard inflation ($w<-1$), if $\delta$ is negative. In the absence of (or trivial) coupling between the GB term and the scalars, there is no crossing between the $w< -1$ and $w> -1$ phases, while this is possible with non-trivial GB couplings, even for constant dilaton phase of the standard picture. Within our model, after a sufficient amount of e-folds of expansion, the rolling of both fields $\phi$ and $\sigma$ can be small. In turn, any possible violation of equivalence principle or deviations from the standard general relativity may be small enough to easily satisfy all astrophysical and cosmological constraints. |
2105.00257 | Michelangelo Preti | Francesco Galvagno, Michelangelo Preti | Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers | 44 pages, 5 figures | null | 10.1007/JHEP11(2021)023 | null | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We complete the program of 2012.15792 about perturbative approaches for
$\mathcal{N}=2$ superconformal quiver theories in four dimensions. We consider
several classes of observables in presence of Wilson loops, and we evaluate
them with the help of supersymmetric localization. We compute Wilson loop
vacuum expectation values, correlators of multiple coincident Wilson loops and
one-point functions of chiral operators in presence of them acting as
superconformal defects. We extend this analysis to the most general case
considering chiral operators and multiple Wilson loops scattered in all the
possible ways among the vector multiplets of the quiver. Finally, we identify
twisted and untwisted observables which probe the orbifold of $AdS_5\times S^5$
with the aim of testing possible holographic perspectives of quiver theories in
$\mathcal{N}=2$.
| [
{
"created": "Sat, 1 May 2021 14:20:12 GMT",
"version": "v1"
}
] | 2021-11-24 | [
[
"Galvagno",
"Francesco",
""
],
[
"Preti",
"Michelangelo",
""
]
] | We complete the program of 2012.15792 about perturbative approaches for $\mathcal{N}=2$ superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the possible ways among the vector multiplets of the quiver. Finally, we identify twisted and untwisted observables which probe the orbifold of $AdS_5\times S^5$ with the aim of testing possible holographic perspectives of quiver theories in $\mathcal{N}=2$. |
1404.6713 | Tom Mertens | T. Mertens, I. Cherednikov | On Geometric Scaling of Light-Like Wilson Polygons: Higher Orders in
$\alpha_s$ | 8 pages, 2 figures | Phys.Lett. B734 2014 198-202 | 10.1016/j.physletb.2014.05.059 | null | hep-th math-ph math.MP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We address the scaling behaviour of contour-shape-dependent ultra-violet
singularities of the light-like cusped Wilson loops in Yang-Mills and ${\cal N}
= 4$ super-Yang-Mills theories in the higher orders of the perturbative
expansion. We give the simple arguments to support the idea that identifying of
a special type of non-local infinitesimal shape variations of the light-like
Wilson polygons with the Fr\'echet differentials results in the combined
geometric and renormalization-group evolution equation, which is applicable
beyond the leading order exponentiated Wilson loops.
| [
{
"created": "Sun, 27 Apr 2014 06:23:28 GMT",
"version": "v1"
}
] | 2014-06-17 | [
[
"Mertens",
"T.",
""
],
[
"Cherednikov",
"I.",
""
]
] | We address the scaling behaviour of contour-shape-dependent ultra-violet singularities of the light-like cusped Wilson loops in Yang-Mills and ${\cal N} = 4$ super-Yang-Mills theories in the higher orders of the perturbative expansion. We give the simple arguments to support the idea that identifying of a special type of non-local infinitesimal shape variations of the light-like Wilson polygons with the Fr\'echet differentials results in the combined geometric and renormalization-group evolution equation, which is applicable beyond the leading order exponentiated Wilson loops. |
0807.1737 | F\'abio Diales da Rocha | Steven S. Gubser and Fabio D. Rocha | The gravity dual to a quantum critical point with spontaneous symmetry
breaking | 5 pages, 2 figures | Phys.Rev.Lett.102:061601,2009 | 10.1103/PhysRevLett.102.061601 | PUPT-2275 | hep-th | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider zero temperature solutions to the Abelian Higgs model coupled to
gravity with a negative cosmological constant. With appropriate choices of
parameters, the geometry contains two copies of anti-de Sitter space, one
describing conformal invariance in the ultraviolet, and one in the infrared.
The effective speed of signal propagation is smaller in the infrared. Green's
functions and associated transport coefficients can have unusual power law
scaling in the infrared. We provide an example in which the real part of the
conductivity scales approximately as omega^3.5 for small omega.
| [
{
"created": "Thu, 10 Jul 2008 20:58:59 GMT",
"version": "v1"
}
] | 2009-02-27 | [
[
"Gubser",
"Steven S.",
""
],
[
"Rocha",
"Fabio D.",
""
]
] | We consider zero temperature solutions to the Abelian Higgs model coupled to gravity with a negative cosmological constant. With appropriate choices of parameters, the geometry contains two copies of anti-de Sitter space, one describing conformal invariance in the ultraviolet, and one in the infrared. The effective speed of signal propagation is smaller in the infrared. Green's functions and associated transport coefficients can have unusual power law scaling in the infrared. We provide an example in which the real part of the conductivity scales approximately as omega^3.5 for small omega. |
hep-th/9512146 | Rafael Ferraro | Rafael Ferraro and Claudio Simeone | Canonical Gauges in the Path Integral for Parametrized Systems | 19 pages (TeX manuscript) | J.Math.Phys. 38 (1997) 599 | 10.1063/1.532006 | null | hep-th gr-qc | null | It is well known that --differing from ordinary gauge systems-- canonical
gauges are not admissible in the path integral for parametrized systems. This
is the case for the relativistic particle and gravitation. However, a time
dependent canonical transformation can turn a parametrized system into an
ordinary gauge system. It is shown how to build a canonical transformation such
that the fixation of the new coordinates is equivalent to the fixation of the
original ones; this aim can be achieved only if the Hamiltonian constraint
allows for an intrinsic global time. Thus the resulting action, describing an
ordinary gauge system and allowing for canonical gauges, can be used in the
path integral for the quantum propagator associated with the original
variables.
| [
{
"created": "Tue, 19 Dec 1995 12:22:00 GMT",
"version": "v1"
},
{
"created": "Tue, 19 Dec 1995 12:45:00 GMT",
"version": "v2"
}
] | 2009-10-28 | [
[
"Ferraro",
"Rafael",
""
],
[
"Simeone",
"Claudio",
""
]
] | It is well known that --differing from ordinary gauge systems-- canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent canonical transformation can turn a parametrized system into an ordinary gauge system. It is shown how to build a canonical transformation such that the fixation of the new coordinates is equivalent to the fixation of the original ones; this aim can be achieved only if the Hamiltonian constraint allows for an intrinsic global time. Thus the resulting action, describing an ordinary gauge system and allowing for canonical gauges, can be used in the path integral for the quantum propagator associated with the original variables. |
hep-th/9306048 | Massimo Porrati | Sergio Ferrara and Massimo Porrati | String Phase Transitions in a Strong Magnetic Field | 8 pages | Mod.Phys.Lett.A8:2497-2502,1993 | 10.1142/S0217732393002828 | UCLA/93/TEP/17, NYU-TH.93/06/01 | hep-th | null | We consider open strings in an external constant magnetic field $H$. For an
(infinite) sequence of critical values of $H$ an increasing number of (highest
spin component) states lying on the first Regge trajectory becomes tachyonic.
In the limit of infinite $H$ all these states are tachyons (with a common
tachyonic mass) both in the case of the bosonic string and for the
Neveu-Schwarz sector of the fermionic string. This result generalizes to
extended object the same instability which occurs in ordinary non-Abelian gauge
theories. The Ramond states have always positive square masses as is the case
for ordinary QED. The weak field limit of the mass spectrum is the same as for
a field theory with gyromagnetic ratio $g_S=2$ for all charged spin states.
This behavior suggests a phase transition of the string as it has been argued
for the ordinary electroweak theory.
| [
{
"created": "Wed, 9 Jun 1993 12:11:29 GMT",
"version": "v1"
}
] | 2010-11-01 | [
[
"Ferrara",
"Sergio",
""
],
[
"Porrati",
"Massimo",
""
]
] | We consider open strings in an external constant magnetic field $H$. For an (infinite) sequence of critical values of $H$ an increasing number of (highest spin component) states lying on the first Regge trajectory becomes tachyonic. In the limit of infinite $H$ all these states are tachyons (with a common tachyonic mass) both in the case of the bosonic string and for the Neveu-Schwarz sector of the fermionic string. This result generalizes to extended object the same instability which occurs in ordinary non-Abelian gauge theories. The Ramond states have always positive square masses as is the case for ordinary QED. The weak field limit of the mass spectrum is the same as for a field theory with gyromagnetic ratio $g_S=2$ for all charged spin states. This behavior suggests a phase transition of the string as it has been argued for the ordinary electroweak theory. |
hep-th/9608188 | null | Chong-Sun Chu, Pei-Ming Ho and Bruno Zumino | Some Complex Quantum Manifolds and their Geometry | Cargese lectures, July 1996, one figure, Full postscript available
from http://theor1.lbl.gov/www/theorgroup/papers/39275.ps | null | null | LBL-39275, UCB-PTH-96/38 | hep-th | null | After recalling briefly some basic properties of the quantum group $GL_q(2)$,
we study the quantum sphere $S_q^2$, quantum projective space $CP_q(N)$ and
quantum Grassmannians as examples of complex (K\"{a}hler) quantum manifolds.
The differential and integral calculus on these manifolds are discussed. It is
shown that many relations of classical projective geometry generalize to the
quantum case. For the case of the quantum sphere a comparison is made with A.
Connes' method.
| [
{
"created": "Thu, 29 Aug 1996 01:21:16 GMT",
"version": "v1"
}
] | 2007-05-23 | [
[
"Chu",
"Chong-Sun",
""
],
[
"Ho",
"Pei-Ming",
""
],
[
"Zumino",
"Bruno",
""
]
] | After recalling briefly some basic properties of the quantum group $GL_q(2)$, we study the quantum sphere $S_q^2$, quantum projective space $CP_q(N)$ and quantum Grassmannians as examples of complex (K\"{a}hler) quantum manifolds. The differential and integral calculus on these manifolds are discussed. It is shown that many relations of classical projective geometry generalize to the quantum case. For the case of the quantum sphere a comparison is made with A. Connes' method. |
1912.11752 | Mikhail Plyushchay | Luis Inzunza, Mikhail S. Plyushchay, Andreas Wipf | Conformal bridge between asymptotic freedom and confinement | 25 pages, comments and refs added, title slightly modified by the
Editor of PRD | Phys. Rev. D 101, 105019 (2020) | 10.1103/PhysRevD.101.105019 | null | hep-th math-ph math.MP quant-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We construct a nonunitary transformation that relates a given "asymptotically
free" conformal quantum mechanical system $H_f$ with its confined, harmonically
trapped version $H_c$. In our construction, Jordan states corresponding to the
zero eigenvalue of $H_f$, as well as its eigenstates and Gaussian packets are
mapped into the eigenstates, coherent states and squeezed states of $H_c$,
respectively. The transformation is an automorphism of the conformal
$\mathfrak{sl}(2,{\mathbb R})$ algebra of the nature of the fourth-order root
of the identity transformation, to which a complex canonical transformation
corresponds on the classical level being the fourth-order root of the spatial
reflection. We investigate the one- and two-dimensional examples that reveal,
in particular, a curious relation between the two-dimensional free particle and
the Landau problem.
| [
{
"created": "Thu, 26 Dec 2019 02:45:37 GMT",
"version": "v1"
},
{
"created": "Tue, 7 Jan 2020 12:18:47 GMT",
"version": "v2"
},
{
"created": "Sat, 30 May 2020 06:29:33 GMT",
"version": "v3"
}
] | 2020-06-03 | [
[
"Inzunza",
"Luis",
""
],
[
"Plyushchay",
"Mikhail S.",
""
],
[
"Wipf",
"Andreas",
""
]
] | We construct a nonunitary transformation that relates a given "asymptotically free" conformal quantum mechanical system $H_f$ with its confined, harmonically trapped version $H_c$. In our construction, Jordan states corresponding to the zero eigenvalue of $H_f$, as well as its eigenstates and Gaussian packets are mapped into the eigenstates, coherent states and squeezed states of $H_c$, respectively. The transformation is an automorphism of the conformal $\mathfrak{sl}(2,{\mathbb R})$ algebra of the nature of the fourth-order root of the identity transformation, to which a complex canonical transformation corresponds on the classical level being the fourth-order root of the spatial reflection. We investigate the one- and two-dimensional examples that reveal, in particular, a curious relation between the two-dimensional free particle and the Landau problem. |
1001.3378 | Enrique Moreno | A. R. Lugo, E. F. Moreno, F. A. Schaposnik | Holographic phase transition from dyons in an AdS black hole background | 19 pages, 7 figures. Minor corrections, references added. Version
published in JHEP. | JHEP03(2010)013 | 10.1007/JHEP03(2010)013 | null | hep-th cond-mat.str-el | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We construct a dyon solution for a Yang-Mills-Higgs theory in a 4 dimensional
Schwarzschild-anti-de Sitter black hole background with temperature T. We then
apply the AdS/CFT correspondence to describe the strong coupling regime of a
2+1 quantum field theory which undergoes a phase transition exhibiting the
condensation of a composite charge operator below a critical temperature $T_c$.
| [
{
"created": "Tue, 19 Jan 2010 20:40:09 GMT",
"version": "v1"
},
{
"created": "Wed, 10 Mar 2010 21:27:16 GMT",
"version": "v2"
}
] | 2015-05-18 | [
[
"Lugo",
"A. R.",
""
],
[
"Moreno",
"E. F.",
""
],
[
"Schaposnik",
"F. A.",
""
]
] | We construct a dyon solution for a Yang-Mills-Higgs theory in a 4 dimensional Schwarzschild-anti-de Sitter black hole background with temperature T. We then apply the AdS/CFT correspondence to describe the strong coupling regime of a 2+1 quantum field theory which undergoes a phase transition exhibiting the condensation of a composite charge operator below a critical temperature $T_c$. |
2111.13223 | Maximilian Rupprecht | Maximilian Rupprecht | The coupling flow of ${\cal N}=4$ super Yang-Mills theory | 17 pages + appendices; v2: minor corrections and clarifications,
matches published version | null | 10.1007/JHEP04(2022)004 | null | hep-th math-ph math.MP | http://creativecommons.org/licenses/by/4.0/ | We offer a novel perspective on ${\cal N}=4$ supersymmetric Yang-Mills (SYM)
theory through the framework of the Nicolai map, a transformation of the
bosonic fields that allows one to compute quantum correlators in terms of a
free, purely bosonic functional measure. Generally, any Nicolai map is obtained
through a path-ordered exponential of the so-called coupling flow operator. The
latter can be canonically constructed in any gauge using an ${\cal N}=1$
off-shell superfield formulation of ${\cal N}=4$ SYM, or alternatively through
dimensional reduction of the result from ${\cal N}=1$ $D=10$ SYM, in which case
we need to restrict to the Landau gauge. We propose a general theory of the
${\cal N}=4$ coupling flow operator, arguing that it exhibits an ambiguity in
form of an R-symmetry freedom given by the Lie algebra $\mathfrak{su}(4)$. This
theory incorporates our two construction approaches as special points in
$\mathfrak{su}(4)$ and defines a broad class of Nicolai maps for ${\cal N}=4$
SYM.
| [
{
"created": "Thu, 25 Nov 2021 19:00:07 GMT",
"version": "v1"
},
{
"created": "Thu, 31 Mar 2022 11:24:42 GMT",
"version": "v2"
}
] | 2022-04-06 | [
[
"Rupprecht",
"Maximilian",
""
]
] | We offer a novel perspective on ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory through the framework of the Nicolai map, a transformation of the bosonic fields that allows one to compute quantum correlators in terms of a free, purely bosonic functional measure. Generally, any Nicolai map is obtained through a path-ordered exponential of the so-called coupling flow operator. The latter can be canonically constructed in any gauge using an ${\cal N}=1$ off-shell superfield formulation of ${\cal N}=4$ SYM, or alternatively through dimensional reduction of the result from ${\cal N}=1$ $D=10$ SYM, in which case we need to restrict to the Landau gauge. We propose a general theory of the ${\cal N}=4$ coupling flow operator, arguing that it exhibits an ambiguity in form of an R-symmetry freedom given by the Lie algebra $\mathfrak{su}(4)$. This theory incorporates our two construction approaches as special points in $\mathfrak{su}(4)$ and defines a broad class of Nicolai maps for ${\cal N}=4$ SYM. |
hep-th/0412121 | Jose Magpantay | Jose A. Magpantay | Effective Quantum Dynamics of Quarks and Gluons in a Stochastic
Background | 17 pages, bbl references added | null | null | null | hep-th | null | The quantum dynamics of quarks, gluons and the scalar degrees of freedom
associated with the non-linear regime of the non-linear gauge is derived. We
discuss the subtleties in quantizing in a stochastic background. Then we show
in detail that the stochastic average of the Yang-Mills action is only
dependent on the gluon and not on the scalars thus proving that the scalars are
non-propagating. Integrating out the scalars from the stochastically averaged
fermion action leads to fermions that decline exponentially. Finally, we derive
the effective action of the gluons and fermions resulting from stochastic
averaging. We show that it leads to a confining four-fermi interaction.
| [
{
"created": "Mon, 13 Dec 2004 05:50:47 GMT",
"version": "v1"
},
{
"created": "Tue, 14 Dec 2004 04:25:28 GMT",
"version": "v2"
}
] | 2007-05-23 | [
[
"Magpantay",
"Jose A.",
""
]
] | The quantum dynamics of quarks, gluons and the scalar degrees of freedom associated with the non-linear regime of the non-linear gauge is derived. We discuss the subtleties in quantizing in a stochastic background. Then we show in detail that the stochastic average of the Yang-Mills action is only dependent on the gluon and not on the scalars thus proving that the scalars are non-propagating. Integrating out the scalars from the stochastically averaged fermion action leads to fermions that decline exponentially. Finally, we derive the effective action of the gluons and fermions resulting from stochastic averaging. We show that it leads to a confining four-fermi interaction. |
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