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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1611.04570
|
Ryosuke Sato
|
Kfir Blum, Masazumi Honda, Ryosuke Sato, Masahiro Takimoto and Kohsaku
Tobioka
|
O($N$) Invariance of the Multi-Field Bounce
|
10 pages, 1 figure: v3: match journal version
| null |
10.1007/JHEP05(2017)109
| null |
hep-th hep-ph math-ph math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
In his 1977 paper on vacuum decay in field theory: The Fate of the False
Vacuum, Coleman considered the problem of a single scalar field and assumed
that the minimum action tunnelling field configuration, the bounce, is
invariant under O(4) rotations in Euclidean space. A proof of the O(4)
invariance of the bounce was provided later by Coleman, Glaser, and Martin
(CGM), who extended the proof to $N>2$ Euclidean dimensions but, again,
restricted non-trivially to a single scalar field. As far as we know a proof of
O($N$) invariance of the bounce for the tunnelling problem with multiple scalar
fields has not been reported, even though it was assumed in many works since,
being of phenomenological interest. We make progress towards closing this gap.
Following CGM we define the reduced problem of finding a field configuration
minimizing the kinetic energy at fixed potential energy. Given a solution of
the reduced problem, the minimum action bounce can always be obtained from it
by means of a scale transformation. We show that if a solution of the reduced
problem exists, then it and the minimum action bounce derived from it are
indeed O($N$) symmetric.
|
[
{
"created": "Mon, 14 Nov 2016 20:47:55 GMT",
"version": "v1"
},
{
"created": "Fri, 9 Dec 2016 14:59:07 GMT",
"version": "v2"
},
{
"created": "Sat, 8 Jul 2017 13:31:18 GMT",
"version": "v3"
}
] |
2017-07-11
|
[
[
"Blum",
"Kfir",
""
],
[
"Honda",
"Masazumi",
""
],
[
"Sato",
"Ryosuke",
""
],
[
"Takimoto",
"Masahiro",
""
],
[
"Tobioka",
"Kohsaku",
""
]
] |
In his 1977 paper on vacuum decay in field theory: The Fate of the False Vacuum, Coleman considered the problem of a single scalar field and assumed that the minimum action tunnelling field configuration, the bounce, is invariant under O(4) rotations in Euclidean space. A proof of the O(4) invariance of the bounce was provided later by Coleman, Glaser, and Martin (CGM), who extended the proof to $N>2$ Euclidean dimensions but, again, restricted non-trivially to a single scalar field. As far as we know a proof of O($N$) invariance of the bounce for the tunnelling problem with multiple scalar fields has not been reported, even though it was assumed in many works since, being of phenomenological interest. We make progress towards closing this gap. Following CGM we define the reduced problem of finding a field configuration minimizing the kinetic energy at fixed potential energy. Given a solution of the reduced problem, the minimum action bounce can always be obtained from it by means of a scale transformation. We show that if a solution of the reduced problem exists, then it and the minimum action bounce derived from it are indeed O($N$) symmetric.
|
1211.2815
|
Blaise Gout\'eraux
|
Marco M. Caldarelli, Joan Camps, Blaise Gout\'eraux and Kostas
Skenderis
|
AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
|
v3: Matches published version
|
Phys. Rev. D 87, 061502(R) (2013)
|
10.1103/PhysRevD.87.061502
|
CCTP-2012-25, CPHT-RR076.1112, DCPT-12/45, LPT-ORSAY 12-108,
NORDITA-2012-87
|
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We show that for every asymptotically AdS solution compactified on a torus
there is a corresponding Ricci-flat solution obtained by replacing the torus by
a sphere, performing a Weyl rescaling of the metric and appropriately
analytically continuing the dimension of the torus/sphere (as in generalized
dimensional reduction). In particular, it maps Minkowski spacetime to AdS on a
torus, the holographic stress energy tensor of AdS to the stress energy tensor
due to a brane localized in the interior of spacetime and AdS black branes to
(asymptotically flat) Schwarzschild black branes. Applying it to the known
solutions describing the hydrodynamic regime in AdS/CFT, we derive the
hydrodynamic stress-tensor of asymptotically flat black branes to second order,
which is constrained by the parent conformal symmetry. We compute the
dispersion relation of the Gregory-Laflamme unstable modes through cubic order
in the wavenumber, finding remarkable agreement with numerical data. In the
case of no transverse sphere, AdS black branes are mapped to Rindler spacetime
and the second-order transport coefficients of the fluid dual to Rindler
spacetime are recovered.
|
[
{
"created": "Mon, 12 Nov 2012 21:00:07 GMT",
"version": "v1"
},
{
"created": "Thu, 29 Nov 2012 20:49:36 GMT",
"version": "v2"
},
{
"created": "Wed, 20 Mar 2013 19:43:19 GMT",
"version": "v3"
}
] |
2013-03-21
|
[
[
"Caldarelli",
"Marco M.",
""
],
[
"Camps",
"Joan",
""
],
[
"Goutéraux",
"Blaise",
""
],
[
"Skenderis",
"Kostas",
""
]
] |
We show that for every asymptotically AdS solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere (as in generalized dimensional reduction). In particular, it maps Minkowski spacetime to AdS on a torus, the holographic stress energy tensor of AdS to the stress energy tensor due to a brane localized in the interior of spacetime and AdS black branes to (asymptotically flat) Schwarzschild black branes. Applying it to the known solutions describing the hydrodynamic regime in AdS/CFT, we derive the hydrodynamic stress-tensor of asymptotically flat black branes to second order, which is constrained by the parent conformal symmetry. We compute the dispersion relation of the Gregory-Laflamme unstable modes through cubic order in the wavenumber, finding remarkable agreement with numerical data. In the case of no transverse sphere, AdS black branes are mapped to Rindler spacetime and the second-order transport coefficients of the fluid dual to Rindler spacetime are recovered.
|
hep-th/9511012
| null |
K. Chadan, R. Kobayashi, A. Martin and J. Stubbe
|
Generalization of the Calogero-Cohn Bound on the Number of Bound States
|
1 page. Correctly formatted version (replaces previous version)
| null |
10.1063/1.531450
|
CERN-TH/95-152
|
hep-th
| null |
It is shown that for the Calogero-Cohn type upper bounds on the number of
bound states of a negative spherically symmetric potential $V(r)$, in each
angular momentum state, that is, bounds containing only the integral
$\int^\infty_0 |V(r)|^{1/2}dr$, the condition $V'(r) \geq 0$ is not necessary,
and can be replaced by the less stringent condition $(d/dr)[r^{1-2p}(-V)^{1-p}]
\leq 0, 1/2 \leq p < 1$, which allows oscillations in the potential. The
constants in the bounds are accordingly modified, depend on $p$ and $\ell$, and
tend to the standard value for $p = 1/2$.
|
[
{
"created": "Thu, 2 Nov 1995 15:02:18 GMT",
"version": "v1"
},
{
"created": "Mon, 13 Nov 1995 09:59:37 GMT",
"version": "v2"
}
] |
2009-10-28
|
[
[
"Chadan",
"K.",
""
],
[
"Kobayashi",
"R.",
""
],
[
"Martin",
"A.",
""
],
[
"Stubbe",
"J.",
""
]
] |
It is shown that for the Calogero-Cohn type upper bounds on the number of bound states of a negative spherically symmetric potential $V(r)$, in each angular momentum state, that is, bounds containing only the integral $\int^\infty_0 |V(r)|^{1/2}dr$, the condition $V'(r) \geq 0$ is not necessary, and can be replaced by the less stringent condition $(d/dr)[r^{1-2p}(-V)^{1-p}] \leq 0, 1/2 \leq p < 1$, which allows oscillations in the potential. The constants in the bounds are accordingly modified, depend on $p$ and $\ell$, and tend to the standard value for $p = 1/2$.
|
2112.05541
|
Gabrielle Weber
|
A. Melikyan, G. Weber
|
Quantum integrability of a massive anisotropic SU(N) fermionic model
|
9 pages
| null |
10.1016/j.physletb.2022.136934
| null |
hep-th math-ph math.MP nlin.SI
|
http://creativecommons.org/licenses/by-nc-nd/4.0/
|
We consider a general anisotropic massive SU(N) fermionic model, and
investigate its quantum integrability. In particular, by regularizing singular
operator products, we derive a system of equations resulting in the S-matrix
and find some non-trivial solutions. We illustrate our findings on the example
of a SU(3) model, and show that the Yang-Baxter equation is satisfied in the
massless limit for all coupling constants, while in the massive case the
solutions are parameterized in terms of the exceptional solutions to the
eight-vertex model.
|
[
{
"created": "Fri, 10 Dec 2021 13:54:49 GMT",
"version": "v1"
}
] |
2022-02-02
|
[
[
"Melikyan",
"A.",
""
],
[
"Weber",
"G.",
""
]
] |
We consider a general anisotropic massive SU(N) fermionic model, and investigate its quantum integrability. In particular, by regularizing singular operator products, we derive a system of equations resulting in the S-matrix and find some non-trivial solutions. We illustrate our findings on the example of a SU(3) model, and show that the Yang-Baxter equation is satisfied in the massless limit for all coupling constants, while in the massive case the solutions are parameterized in terms of the exceptional solutions to the eight-vertex model.
|
1603.09298
|
Daniel Roberts
|
Daniel A. Roberts, Brian Swingle
|
Lieb-Robinson and the butterfly effect
|
5+5 pages, 0 figures. v2: updated references and additional
clarifications
|
Phys. Rev. Lett. 117, 091602 (2016)
|
10.1103/PhysRevLett.117.091602
|
MIT-CTP/4794
|
hep-th cond-mat.quant-gas cond-mat.str-el quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
As experiments are increasingly able to probe the quantum dynamics of systems
with many degrees of freedom, it is interesting to probe fundamental bounds on
the dynamics of quantum information. We elaborate on the relationship between
one such bound---the Lieb-Robinson bound---and the butterfly effect in
strongly-coupled quantum systems. The butterfly effect implies the ballistic
growth of local operators in time, which can be quantified with the "butterfly"
velocity $v_B$. Similarly, the Lieb-Robinson velocity places a state
independent ballistic upper bound on the size of time evolved operators in
non-relativistic lattice models. Here, we argue that $v_B$ is a state-dependent
effective Lieb-Robinson velocity. We study the butterfly velocity in a wide
variety of quantum field theories using holography and compare with free
particle computations to understand the role of strong coupling. We find that,
depending on the way length and time scale, $v_B$ acquires a temperature
dependence and decreases towards the IR. We also comment on experimental
prospects and on the relationship between the butterfly velocity and signaling.
|
[
{
"created": "Wed, 30 Mar 2016 18:03:37 GMT",
"version": "v1"
},
{
"created": "Wed, 25 May 2016 22:04:38 GMT",
"version": "v2"
}
] |
2016-08-31
|
[
[
"Roberts",
"Daniel A.",
""
],
[
"Swingle",
"Brian",
""
]
] |
As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound---the Lieb-Robinson bound---and the butterfly effect in strongly-coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the "butterfly" velocity $v_B$. Similarly, the Lieb-Robinson velocity places a state independent ballistic upper bound on the size of time evolved operators in non-relativistic lattice models. Here, we argue that $v_B$ is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free particle computations to understand the role of strong coupling. We find that, depending on the way length and time scale, $v_B$ acquires a temperature dependence and decreases towards the IR. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.
|
1001.4324
|
Nikodem Poplawski
|
Nikodem J. Poplawski
|
Einstein-Cartan gravity excludes extra dimensions
|
3 pages
| null | null | null |
hep-th gr-qc hep-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We show that the electron in the Riemann-Cartan spacetime with extra
dimensions has a finite size that is much larger than the experimental upper
limit on its radius. Thus the Arkani-Hamed-Dimopoulos-Dvali and Randall-Sundrum
models of the weak/Planck hierarchy in particle physics are not viable if spin
produces torsion according to the Einstein-Cartan theory of gravity.
|
[
{
"created": "Mon, 25 Jan 2010 07:06:38 GMT",
"version": "v1"
}
] |
2010-01-26
|
[
[
"Poplawski",
"Nikodem J.",
""
]
] |
We show that the electron in the Riemann-Cartan spacetime with extra dimensions has a finite size that is much larger than the experimental upper limit on its radius. Thus the Arkani-Hamed-Dimopoulos-Dvali and Randall-Sundrum models of the weak/Planck hierarchy in particle physics are not viable if spin produces torsion according to the Einstein-Cartan theory of gravity.
|
2404.10695
|
Claudia Rella
|
Veronica Fantini and Claudia Rella
|
Strong-weak symmetry and quantum modularity of resurgent topological
strings on local $\mathbb{P}^2$
|
52 pages, 3 figures
| null | null | null |
hep-th math-ph math.AG math.MP math.NT
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Quantizing the mirror curve to a toric Calabi-Yau threefold gives rise to
quantum operators whose fermionic spectral traces produce factorially divergent
formal power series in the Planck constant and its inverse. These are
conjecturally captured by the Nekrasov-Shatashvili and standard topological
string free energies, respectively, via the TS/ST correspondence. The resurgent
structures of the first fermionic spectral trace of local $\mathbb{P}^2$ in
both weak and strong coupling limits were solved exactly by the second author
in [1]. Here, we take the perspective of the Stokes constants and their
generating functions. We prove that a full-fledged strong-weak resurgent
symmetry is at play, exchanging the perturbative/nonperturbative contributions
to the holomorphic and anti-holomorphic blocks in the factorization of the
spectral trace. This relies on a global net of relations connecting the
perturbative series and the discontinuities in the dual regimes, which is built
upon the analytic properties of the $L$-functions with coefficients given by
the Stokes constants and the $q$-series acting as their generating functions.
Then, we show that the latter are holomorphic quantum modular forms for
$\Gamma_1(3)$ and are reconstructed by the median resummation of their
asymptotic expansions.
|
[
{
"created": "Tue, 16 Apr 2024 16:14:53 GMT",
"version": "v1"
}
] |
2024-04-17
|
[
[
"Fantini",
"Veronica",
""
],
[
"Rella",
"Claudia",
""
]
] |
Quantizing the mirror curve to a toric Calabi-Yau threefold gives rise to quantum operators whose fermionic spectral traces produce factorially divergent formal power series in the Planck constant and its inverse. These are conjecturally captured by the Nekrasov-Shatashvili and standard topological string free energies, respectively, via the TS/ST correspondence. The resurgent structures of the first fermionic spectral trace of local $\mathbb{P}^2$ in both weak and strong coupling limits were solved exactly by the second author in [1]. Here, we take the perspective of the Stokes constants and their generating functions. We prove that a full-fledged strong-weak resurgent symmetry is at play, exchanging the perturbative/nonperturbative contributions to the holomorphic and anti-holomorphic blocks in the factorization of the spectral trace. This relies on a global net of relations connecting the perturbative series and the discontinuities in the dual regimes, which is built upon the analytic properties of the $L$-functions with coefficients given by the Stokes constants and the $q$-series acting as their generating functions. Then, we show that the latter are holomorphic quantum modular forms for $\Gamma_1(3)$ and are reconstructed by the median resummation of their asymptotic expansions.
|
0804.4793
|
Hisayuki Sato
|
H.Sato and N.Sawado
|
SU(3) dibaryons in the Einstein-Skyrme model
|
9 pages, 14 figures
|
Phys.Lett.B660:72-79,2008
|
10.1016/j.physletb.2007.10.084
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
SU(3) collective coordinate quantization to the regular solution of the B=2
axially symmetric Einstein-Skyrme system is performed. For the symmetry
breaking term, a perturbative treatment as well as the exact diagonalization
method called Yabu-Ando approach are used. The effect of the gravity on the
mass spectra of the SU(3) dibaryons and the symmetry breaking term is studied
in detail. In the strong gravity limit, the symmetry breaking term
significantly reduces and exact SU(3) flavor symmetry is recovered.
|
[
{
"created": "Wed, 30 Apr 2008 11:19:14 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Sato",
"H.",
""
],
[
"Sawado",
"N.",
""
]
] |
SU(3) collective coordinate quantization to the regular solution of the B=2 axially symmetric Einstein-Skyrme system is performed. For the symmetry breaking term, a perturbative treatment as well as the exact diagonalization method called Yabu-Ando approach are used. The effect of the gravity on the mass spectra of the SU(3) dibaryons and the symmetry breaking term is studied in detail. In the strong gravity limit, the symmetry breaking term significantly reduces and exact SU(3) flavor symmetry is recovered.
|
2311.03462
|
Spencer Tamagni
|
Spencer Tamagni
|
Stable Envelopes, Vortex Moduli Spaces, and Verma Modules
|
41 pages, 1 figure
| null | null | null |
hep-th math.AG math.RT
|
http://creativecommons.org/licenses/by/4.0/
|
We explicitly construct K-theoretic and elliptic stable envelopes for certain
moduli spaces of vortices, and apply this to enumerative geometry of rational
curves in these varieties. In particular, we identify the quantum difference
equations in equivariant variables with quantum Knizhnik-Zamolodchikov
equations, and give their monodromy in terms of geometric elliptic R-matrices.
A novel geometric feature in these constructions is that the varieties under
study are not holomorphic symplectic, yet nonetheless have
representation-theoretic significance. In physics, they originate from 3d
supersymmetric gauge theories with $\mathcal{N} = 2$ rather than $\mathcal{N} =
4$ supersymmetry. We discuss an application of the results to the ramified
version of the quantum q-Langlands correspondence of Aganagic, Frenkel, and
Okounkov.
|
[
{
"created": "Mon, 6 Nov 2023 19:02:51 GMT",
"version": "v1"
}
] |
2023-11-08
|
[
[
"Tamagni",
"Spencer",
""
]
] |
We explicitly construct K-theoretic and elliptic stable envelopes for certain moduli spaces of vortices, and apply this to enumerative geometry of rational curves in these varieties. In particular, we identify the quantum difference equations in equivariant variables with quantum Knizhnik-Zamolodchikov equations, and give their monodromy in terms of geometric elliptic R-matrices. A novel geometric feature in these constructions is that the varieties under study are not holomorphic symplectic, yet nonetheless have representation-theoretic significance. In physics, they originate from 3d supersymmetric gauge theories with $\mathcal{N} = 2$ rather than $\mathcal{N} = 4$ supersymmetry. We discuss an application of the results to the ramified version of the quantum q-Langlands correspondence of Aganagic, Frenkel, and Okounkov.
|
hep-th/9604106
|
Lawrence Horwitz
|
L. Burakovsky, L.P. Horwitz
|
Mass - Proper Time Uncertainty Relation in a Manifestly Covariant
Relativistic Statistical Mechanics
|
Latex, 13 pages
|
Found.Phys.Lett. 10 (1997) 503-516
| null |
LA-UR-96-1337; IASSNS-96/34
|
hep-th
| null |
We prove the uncertainty relation $T_{\triangle V}\triangle
m\stackrel{>}{\sim }2\pi \hbar /c^2,$ which is realized on a statistical
mechanical level for an ensemble of events in $(1+D)$-dimensional spacetime
with motion parametrized by an invariant ``proper time'' $\tau ,$ where
$T_{\triangle V}$ is the average passage interval in $\tau $ for the events
which pass through a small (typical) $(1+D)$-volume $\triangle V,$ and
$\triangle m$ is the dispersion of mass around its on-shell value in such an
ensemble. We show that a linear mass spectrum is a completely general property
of a $(1+D)$-dimensional off-shell theory.
|
[
{
"created": "Thu, 18 Apr 1996 19:06:38 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Burakovsky",
"L.",
""
],
[
"Horwitz",
"L. P.",
""
]
] |
We prove the uncertainty relation $T_{\triangle V}\triangle m\stackrel{>}{\sim }2\pi \hbar /c^2,$ which is realized on a statistical mechanical level for an ensemble of events in $(1+D)$-dimensional spacetime with motion parametrized by an invariant ``proper time'' $\tau ,$ where $T_{\triangle V}$ is the average passage interval in $\tau $ for the events which pass through a small (typical) $(1+D)$-volume $\triangle V,$ and $\triangle m$ is the dispersion of mass around its on-shell value in such an ensemble. We show that a linear mass spectrum is a completely general property of a $(1+D)$-dimensional off-shell theory.
|
2311.01277
|
Marcin Pi\k{a}tek dr.
|
Neda Abbasi Taklimi, Franco Ferrari, Marcin R. Piatek
|
Self-dual solutions of a field theory model of two linked rings
|
27 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1605.03920 by other authors
| null | null | null |
hep-th
|
http://creativecommons.org/licenses/by/4.0/
|
In this work the connection established in [7, 8] between a model of two
linked polymers rings with fixed Gaussian linking number forming a 4-plat and
the statistical mechanics of non-relativistic anyon particles is explored. The
excluded volume interactions have been switched off and only the interactions
of entropic origin arising from the topological constraints are considered. An
interpretation from the polymer point of view of the field equations that
minimize the energy of the model in the limit in which one of the spatial
dimensions of the 4-plat becomes very large is provided. It is shown that the
self-dual contributions are responsible for the long-range interactions that
are necessary for preserving the global topological properties of the system
during the thermal fluctuations. The non self-dual part is also related to the
topological constraints, and takes into account the local interactions acting
on the monomers in order to prevent the breaking of the polymer lines. It turns
out that the energy landscape of the two linked rings is quite complex.
Assuming as a rough approximation that the monomer densities of half of the
4-plat are constant, at least two points of energy minimum are found. Classes
of non-trivial self-dual solutions of the self-dual field equations are
derived. ... .
|
[
{
"created": "Thu, 2 Nov 2023 14:46:37 GMT",
"version": "v1"
},
{
"created": "Sun, 5 Nov 2023 09:54:09 GMT",
"version": "v2"
}
] |
2023-11-07
|
[
[
"Taklimi",
"Neda Abbasi",
""
],
[
"Ferrari",
"Franco",
""
],
[
"Piatek",
"Marcin R.",
""
]
] |
In this work the connection established in [7, 8] between a model of two linked polymers rings with fixed Gaussian linking number forming a 4-plat and the statistical mechanics of non-relativistic anyon particles is explored. The excluded volume interactions have been switched off and only the interactions of entropic origin arising from the topological constraints are considered. An interpretation from the polymer point of view of the field equations that minimize the energy of the model in the limit in which one of the spatial dimensions of the 4-plat becomes very large is provided. It is shown that the self-dual contributions are responsible for the long-range interactions that are necessary for preserving the global topological properties of the system during the thermal fluctuations. The non self-dual part is also related to the topological constraints, and takes into account the local interactions acting on the monomers in order to prevent the breaking of the polymer lines. It turns out that the energy landscape of the two linked rings is quite complex. Assuming as a rough approximation that the monomer densities of half of the 4-plat are constant, at least two points of energy minimum are found. Classes of non-trivial self-dual solutions of the self-dual field equations are derived. ... .
|
2208.02273
|
M\'at\'e Lencs\'es
|
M. Lencs\'es, G. Mussardo, G. Tak\'acs
|
Variations on vacuum decay: the scaling Ising and tricritical Ising
field theories
|
17 pages, 16 figures, 3 tables
| null |
10.1103/PhysRevD.106.105003
| null |
hep-th cond-mat.stat-mech
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study the decay of the false vacuum in the scaling Ising and tricritical
Ising field theories using the Truncated Conformal Space Approach and compare
the numerical results to theoretical predictions in the thin wall limit. In the
Ising case, the results are consistent with previous studies on the quantum
spin chain and the $\varphi^4$ quantum field theory; in particular we confirm
that while the theoretical predictions get the dependence of the bubble
nucleation rate on the latent heat right, they are off by a model dependent
overall coefficient. The tricritical Ising model allows us on the other hand to
examine more exotic vacuum degeneracy structures, such as three vacua or two
asymmetric vacua, which leads us to study several novel scenarios of false
vacuum decay by lifting the vacuum degeneracy using different perturbations.
|
[
{
"created": "Wed, 3 Aug 2022 18:00:17 GMT",
"version": "v1"
}
] |
2022-11-23
|
[
[
"Lencsés",
"M.",
""
],
[
"Mussardo",
"G.",
""
],
[
"Takács",
"G.",
""
]
] |
We study the decay of the false vacuum in the scaling Ising and tricritical Ising field theories using the Truncated Conformal Space Approach and compare the numerical results to theoretical predictions in the thin wall limit. In the Ising case, the results are consistent with previous studies on the quantum spin chain and the $\varphi^4$ quantum field theory; in particular we confirm that while the theoretical predictions get the dependence of the bubble nucleation rate on the latent heat right, they are off by a model dependent overall coefficient. The tricritical Ising model allows us on the other hand to examine more exotic vacuum degeneracy structures, such as three vacua or two asymmetric vacua, which leads us to study several novel scenarios of false vacuum decay by lifting the vacuum degeneracy using different perturbations.
|
2204.01829
|
Hynek Paul
|
J. M. Drummond, H. Paul
|
Two-loop supergravity on AdS$_5\times$S$^5$ from CFT
|
51 pages, 1 ancillary file; v2: minor modifications, added reference;
v3: extended discussion, published version
|
JHEP 08 (2022) 275
|
10.1007/JHEP08(2022)275
| null |
hep-th
|
http://creativecommons.org/licenses/by/4.0/
|
We describe a construction of the two-loop amplitude of four graviton
supermultiplets in AdS$_5\times$S$^5$. We start from an ansatz for a
preamplitude from which we generate the full amplitude under the action of a
specific Casimir operator. The ansatz captures a recent ansatz of Huang and
Yuan and we confirm their result through similar constraints. The form of the
result suggests that all ambiguities are captured by the preamplitude which
determines the result up to tree-level ambiguities only. We identify a class of
four-dimensional `zigzag' integrals which are perfectly adapted to describing
the leading logarithmic discontinuity to all orders. We also observe that a
bonus crossing symmetry of the preamplitude follows from the transformation
properties of the Casimir operator. Combined with the zigzag integrals this
allows us to construct a crossing symmetric function with the correct leading
logarithmic discontinuities in all channels.
From the two-loop result we extract an explicit expression for the two-loop
correction to the anomalous dimensions of twist-four operators of generic spin
which includes dependence on (alternating) nested harmonic sums up to weight
three. We also revisit the prescription of the bulk-point limit of AdS
amplitudes and show how it recovers the full flat-space amplitude, not just its
discontinuity. With this extended notion of the bulk-point limit we reproduce
the scale-dependent logarithmic threshold terms of type IIB string theory in
flat-space.
|
[
{
"created": "Mon, 4 Apr 2022 20:29:41 GMT",
"version": "v1"
},
{
"created": "Wed, 11 May 2022 15:50:08 GMT",
"version": "v2"
},
{
"created": "Mon, 29 Aug 2022 08:40:35 GMT",
"version": "v3"
}
] |
2022-08-30
|
[
[
"Drummond",
"J. M.",
""
],
[
"Paul",
"H.",
""
]
] |
We describe a construction of the two-loop amplitude of four graviton supermultiplets in AdS$_5\times$S$^5$. We start from an ansatz for a preamplitude from which we generate the full amplitude under the action of a specific Casimir operator. The ansatz captures a recent ansatz of Huang and Yuan and we confirm their result through similar constraints. The form of the result suggests that all ambiguities are captured by the preamplitude which determines the result up to tree-level ambiguities only. We identify a class of four-dimensional `zigzag' integrals which are perfectly adapted to describing the leading logarithmic discontinuity to all orders. We also observe that a bonus crossing symmetry of the preamplitude follows from the transformation properties of the Casimir operator. Combined with the zigzag integrals this allows us to construct a crossing symmetric function with the correct leading logarithmic discontinuities in all channels. From the two-loop result we extract an explicit expression for the two-loop correction to the anomalous dimensions of twist-four operators of generic spin which includes dependence on (alternating) nested harmonic sums up to weight three. We also revisit the prescription of the bulk-point limit of AdS amplitudes and show how it recovers the full flat-space amplitude, not just its discontinuity. With this extended notion of the bulk-point limit we reproduce the scale-dependent logarithmic threshold terms of type IIB string theory in flat-space.
|
hep-th/9305010
|
Blau Matthias
|
M. Blau and G. Thompson
|
Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G
model
|
47 pages (in A4 format), LaTex file, (original was truncated by the
mailer - apologies, m.b.), IC/93/83
|
Nucl.Phys. B408 (1993) 345-390
|
10.1016/0550-3213(93)90538-Z
| null |
hep-th
| null |
We give a derivation of the Verlinde formula for the $G_{k}$ WZW model from
Chern-Simons theory, without taking recourse to CFT, by calculating explicitly
the partition function $Z_{\Sigma\times S^{1}}$ of $\Sigma\times S^{1}$ with an
arbitrary number of labelled punctures. By a suitable gauge choice,
$Z_{\Sigma\times S^{1}}$ is reduced to the partition function of an Abelian
topological field theory on $\Sigma$ (a deformation of non-Abelian BF and
Yang-Mills theory) whose evaluation is straightforward. This relates the
Verlinde formula to the Ray-Singer torsion of $\Sigma\times S^{1}$. We derive
the $G_{k}/G_{k}$ model from Chern-Simons theory, proving their equivalence,
and give an alternative derivation of the Verlinde formula by calculating the
$G_{k}/G_{k}$ path integral via a functional version of the Weyl integral
formula. From this point of view the Verlinde formula arises from the
corresponding Jacobian, the Weyl determinant. Also, a novel derivation of the
shift $k\ra k+h$ is given, based on the index of the twisted Dolbeault complex.
|
[
{
"created": "Tue, 4 May 1993 13:39:34 GMT",
"version": "v1"
},
{
"created": "Wed, 5 May 1993 08:52:21 GMT",
"version": "v2"
}
] |
2009-10-22
|
[
[
"Blau",
"M.",
""
],
[
"Thompson",
"G.",
""
]
] |
We give a derivation of the Verlinde formula for the $G_{k}$ WZW model from Chern-Simons theory, without taking recourse to CFT, by calculating explicitly the partition function $Z_{\Sigma\times S^{1}}$ of $\Sigma\times S^{1}$ with an arbitrary number of labelled punctures. By a suitable gauge choice, $Z_{\Sigma\times S^{1}}$ is reduced to the partition function of an Abelian topological field theory on $\Sigma$ (a deformation of non-Abelian BF and Yang-Mills theory) whose evaluation is straightforward. This relates the Verlinde formula to the Ray-Singer torsion of $\Sigma\times S^{1}$. We derive the $G_{k}/G_{k}$ model from Chern-Simons theory, proving their equivalence, and give an alternative derivation of the Verlinde formula by calculating the $G_{k}/G_{k}$ path integral via a functional version of the Weyl integral formula. From this point of view the Verlinde formula arises from the corresponding Jacobian, the Weyl determinant. Also, a novel derivation of the shift $k\ra k+h$ is given, based on the index of the twisted Dolbeault complex.
|
1703.04714
|
Humberto Gomez
|
Humberto Gomez
|
Quadratic Feynman Loop Integrands From Massless Scattering Equations
|
26 pages, typos fixed and references added
|
Phys. Rev. D 95, 106006 (2017)
|
10.1103/PhysRevD.95.106006
| null |
hep-th math-ph math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Recently the Cachazo-He-Yuan (CHY) approach has been extended to loop level,
but the resulting loop integrand has propagators that are linear in the loop
momentum unlike Feynman's. In this note we present a new technique that
directly produces quadratic propagators identical to Feynman's from the CHY
approach. This paper focuses on $\Phi^3$ theory but extensions to others
theories are briefly discussed. In addition, our proposal has an interesting
geometric meaning, we can interpret this new formula as a unitary cut on a
higher genus Riemann surface.
|
[
{
"created": "Tue, 14 Mar 2017 20:44:56 GMT",
"version": "v1"
},
{
"created": "Wed, 17 May 2017 21:10:08 GMT",
"version": "v2"
}
] |
2017-05-24
|
[
[
"Gomez",
"Humberto",
""
]
] |
Recently the Cachazo-He-Yuan (CHY) approach has been extended to loop level, but the resulting loop integrand has propagators that are linear in the loop momentum unlike Feynman's. In this note we present a new technique that directly produces quadratic propagators identical to Feynman's from the CHY approach. This paper focuses on $\Phi^3$ theory but extensions to others theories are briefly discussed. In addition, our proposal has an interesting geometric meaning, we can interpret this new formula as a unitary cut on a higher genus Riemann surface.
|
1301.0208
|
Changhyun Ahn
|
Changhyun Ahn and Jinsub Paeng
|
The OPEs of Spin-4 Casimir Currents in the Holographic SO(N) Coset
Minimal Models
|
22 pages; the footnote 8 added
| null |
10.1088/0264-9381/30/17/175004
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We compute the operator product expansion (OPE) between the spin-4 current
and itself in the WD_4 coset minimal model with SO(8) current algebra. The
right hand side of this OPE contains the spin-6 Casimir current which is also a
generator of WD_4 coset minimal model. Based on this N=8 result, we generalize
the above OPE for the general N(in the WD_{N/2} coset minimal model) by using
two N-generalized coupling constants initiated by Hornfeck sometime ago: the
simplest OPE for the lowest higher spin currents. We also analyze the similar
OPE in the WB_3(and WB_{(N-1)/2}) coset minimal model with SO(7) current
algebra. The large N 't Hooft limits are discussed. Our results in two
dimensional conformal field theory provide the asymptotic symmetry, at the
quantum level, of the higher spin AdS_3 gravity found by Chen et al.
|
[
{
"created": "Wed, 2 Jan 2013 11:02:04 GMT",
"version": "v1"
},
{
"created": "Mon, 4 Mar 2013 12:19:39 GMT",
"version": "v2"
}
] |
2015-06-12
|
[
[
"Ahn",
"Changhyun",
""
],
[
"Paeng",
"Jinsub",
""
]
] |
We compute the operator product expansion (OPE) between the spin-4 current and itself in the WD_4 coset minimal model with SO(8) current algebra. The right hand side of this OPE contains the spin-6 Casimir current which is also a generator of WD_4 coset minimal model. Based on this N=8 result, we generalize the above OPE for the general N(in the WD_{N/2} coset minimal model) by using two N-generalized coupling constants initiated by Hornfeck sometime ago: the simplest OPE for the lowest higher spin currents. We also analyze the similar OPE in the WB_3(and WB_{(N-1)/2}) coset minimal model with SO(7) current algebra. The large N 't Hooft limits are discussed. Our results in two dimensional conformal field theory provide the asymptotic symmetry, at the quantum level, of the higher spin AdS_3 gravity found by Chen et al.
|
hep-th/9812015
|
Philippe Pouliot
|
Philippe Pouliot
|
Molien Function for Duality
|
6 pages, clarifications to sections 3,4 and a reference added, thanks
to O. Aharony, C. Cummins and A. Schwimmer
|
JHEP 9901:021,1999
|
10.1088/1126-6708/1999/01/021
| null |
hep-th
| null |
The Molien function counts the number of independent group invariants of a
representation. For chiral superfields, it is invariant under duality by
construction. We illustrate how it calculates the spectrum of supersymmetric
gauge theories.
|
[
{
"created": "Wed, 2 Dec 1998 04:54:57 GMT",
"version": "v1"
},
{
"created": "Thu, 21 Jan 1999 18:19:17 GMT",
"version": "v2"
}
] |
2010-02-03
|
[
[
"Pouliot",
"Philippe",
""
]
] |
The Molien function counts the number of independent group invariants of a representation. For chiral superfields, it is invariant under duality by construction. We illustrate how it calculates the spectrum of supersymmetric gauge theories.
|
2304.10239
|
Alexander S\"oderberg Rousu
|
Alexander S\"oderberg Rousu
|
Fusion of conformal defects in interacting theories
|
31 pages, 8 figures
| null | null |
UUITP-09/23
|
hep-th cond-mat.stat-mech
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study fusion of two scalar Wilson defects. We propose that fusion holds at
a quantum level by showing that bare one-point functions stay invariant. This
is an expected result as the path integral stays invariant under fusion of the
two defects. The difference instead lies in renormalization of local quantities
on the defects. Those on the fused defect takes into account UV divergences in
the fusion limit when the two defects approach eachother, in addition to UV
divergences in the coincident limit of defect-local fields and in the near
defect limits of bulk-local fields. At the fixed point of the corresponding RG
flow the two conformal defects have fused into a single conformal defect.
|
[
{
"created": "Thu, 20 Apr 2023 11:57:47 GMT",
"version": "v1"
}
] |
2023-04-21
|
[
[
"Rousu",
"Alexander Söderberg",
""
]
] |
We study fusion of two scalar Wilson defects. We propose that fusion holds at a quantum level by showing that bare one-point functions stay invariant. This is an expected result as the path integral stays invariant under fusion of the two defects. The difference instead lies in renormalization of local quantities on the defects. Those on the fused defect takes into account UV divergences in the fusion limit when the two defects approach eachother, in addition to UV divergences in the coincident limit of defect-local fields and in the near defect limits of bulk-local fields. At the fixed point of the corresponding RG flow the two conformal defects have fused into a single conformal defect.
|
hep-th/9812024
|
Ori Ganor
|
Ori J. Ganor
|
U-duality Twists and Possible Phase Transitions in 2+1D Supergravity
|
40pp TeX, a typo corrected and references added
|
Nucl.Phys.B549:145-180,1999
|
10.1016/S0550-3213(99)00108-X
|
PUPT-1792
|
hep-th
| null |
We study 2+1D toroidal compactifications of M-theory with twists in the
U-duality group. These compactifications realize many symmetric-manifolds from
the classification of 2+1D extended supergravity moduli-spaces. We then focus
on the moduli-space $SU(2,1)/U(2)$ obtained by dimensional reduction of pure
N=2 supergravity in 3+1D. This space is realized with an explicit example.
Assuming that there are no quantum corrections, we conjecture that the
classical discrete duality group has to be augmented with an extra strong/weak
coupling duality. This implies the existence of new phases of the theory in
which the original 8 compactification radii are all fixed at the Planck scale.
|
[
{
"created": "Wed, 2 Dec 1998 17:05:45 GMT",
"version": "v1"
},
{
"created": "Mon, 14 Dec 1998 15:13:13 GMT",
"version": "v2"
}
] |
2010-11-19
|
[
[
"Ganor",
"Ori J.",
""
]
] |
We study 2+1D toroidal compactifications of M-theory with twists in the U-duality group. These compactifications realize many symmetric-manifolds from the classification of 2+1D extended supergravity moduli-spaces. We then focus on the moduli-space $SU(2,1)/U(2)$ obtained by dimensional reduction of pure N=2 supergravity in 3+1D. This space is realized with an explicit example. Assuming that there are no quantum corrections, we conjecture that the classical discrete duality group has to be augmented with an extra strong/weak coupling duality. This implies the existence of new phases of the theory in which the original 8 compactification radii are all fixed at the Planck scale.
|
hep-th/0410005
|
Laura Andrianopoli
|
L. Andrianopoli, S. Ferrara, M.A. Lledo'
|
Generalized dimensional reduction of supergravity with eight
supercharges
|
Contribution to the proceedings of ``NathFest'' at PASCOS conference,
Northeastern University, Boston, Ma, August 2004
| null |
10.1142/9789812701756_0092
| null |
hep-th
| null |
We describe some recent investigation about the structure of generic D=4,5
theories obtained by generalized dimensional reduction of D=5,6 theories with
eight supercharges. We relate the Scherk-Schwarz reduction to a special class
of N=2 no-scale gauged supergravities.
|
[
{
"created": "Fri, 1 Oct 2004 08:23:05 GMT",
"version": "v1"
}
] |
2017-08-23
|
[
[
"Andrianopoli",
"L.",
""
],
[
"Ferrara",
"S.",
""
],
[
"Lledo'",
"M. A.",
""
]
] |
We describe some recent investigation about the structure of generic D=4,5 theories obtained by generalized dimensional reduction of D=5,6 theories with eight supercharges. We relate the Scherk-Schwarz reduction to a special class of N=2 no-scale gauged supergravities.
|
hep-th/9804133
|
Helmuth Hueffel
|
Helmuth Huffel and Gerald Kelnhofer
|
Generalized Stochastic Quantization of Yang-Mills Theory
|
19 pages, Latex
|
Annals Phys. 270 (1998) 231-245
|
10.1006/aphy.1998.5851
|
University of Vienna preprint UWThPh-1998-4
|
hep-th
| null |
We perform the stochastic quantization of Yang-Mills theory in configuration
space and derive the Faddeev-Popov path integral density. Based on a
generalization of the stochastic gauge fixing scheme and its geometrical
interpretation this result is obtained as the exact equilibrium solution of the
associated Fokker--Planck equation. Included in our discussion is the precise
range of validity of our approach.
|
[
{
"created": "Mon, 20 Apr 1998 17:03:06 GMT",
"version": "v1"
}
] |
2009-10-31
|
[
[
"Huffel",
"Helmuth",
""
],
[
"Kelnhofer",
"Gerald",
""
]
] |
We perform the stochastic quantization of Yang-Mills theory in configuration space and derive the Faddeev-Popov path integral density. Based on a generalization of the stochastic gauge fixing scheme and its geometrical interpretation this result is obtained as the exact equilibrium solution of the associated Fokker--Planck equation. Included in our discussion is the precise range of validity of our approach.
|
2204.00569
|
Arne Lykke Larsen
|
Arne Lykke Larsen
|
Considering the two Spin and the two Angular Momenta String Solutions in
$AdS_5 \times S^5$
|
26 pages, text overlap with itself
| null | null | null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
In this paper, we consider two almost opposite sectors of actual string
configuration ans\"atze in $AdS_5\times S^5$, which anyway have almost the same
features: The two spin solution, which has constant angles in $S^5$ and the two
angular momenta solution, which has constant "angels" in $AdS_5$, however for
the two angular momenta solution, we have to take the time coordinate from
$AdS_5$, thus there is a little asymmetry between the two string configurations
in $AdS_5\times S^5$. Without being autistic, there is around $69$ equations
between the similar equations in the two sectors, compare equations (34) and
(104) and also compare equations (64) and (134). Again, without being autistic,
the text after the equations in the two sectors, is almost precisely the same.
In our notation, the difference between the two sectors is as follows;
$\rho\leftrightarrow \theta$, $\phi \leftrightarrow \psi$, $\sinh\rho
\leftrightarrow \sin\theta$, $y_i\leftrightarrow x_i$, $y \leftrightarrow x$
etc. The string configurations of this paper, are both solvable by the Neumann
System. However, our setup in this paper is generally for the
Neumann-Rosochatius System, which is also solvable, since we intend to
generalize our results from the Neumann System to the Neumann-Rosochatius
System and to several types of deformed Neumann-Rosochatius Systems. In the
second part of this paper, which is independent of any string configurations in
$AdS_5\times S^5$ and concerns String Cosmology in $D=10$ dimensions. I will
seriously argue that there was no Big Bang; I truly believe that the Universe
has been there forever, see True Conclusions, Section 10.
|
[
{
"created": "Fri, 1 Apr 2022 16:54:40 GMT",
"version": "v1"
},
{
"created": "Tue, 19 Apr 2022 15:26:35 GMT",
"version": "v2"
}
] |
2022-04-27
|
[
[
"Larsen",
"Arne Lykke",
""
]
] |
In this paper, we consider two almost opposite sectors of actual string configuration ans\"atze in $AdS_5\times S^5$, which anyway have almost the same features: The two spin solution, which has constant angles in $S^5$ and the two angular momenta solution, which has constant "angels" in $AdS_5$, however for the two angular momenta solution, we have to take the time coordinate from $AdS_5$, thus there is a little asymmetry between the two string configurations in $AdS_5\times S^5$. Without being autistic, there is around $69$ equations between the similar equations in the two sectors, compare equations (34) and (104) and also compare equations (64) and (134). Again, without being autistic, the text after the equations in the two sectors, is almost precisely the same. In our notation, the difference between the two sectors is as follows; $\rho\leftrightarrow \theta$, $\phi \leftrightarrow \psi$, $\sinh\rho \leftrightarrow \sin\theta$, $y_i\leftrightarrow x_i$, $y \leftrightarrow x$ etc. The string configurations of this paper, are both solvable by the Neumann System. However, our setup in this paper is generally for the Neumann-Rosochatius System, which is also solvable, since we intend to generalize our results from the Neumann System to the Neumann-Rosochatius System and to several types of deformed Neumann-Rosochatius Systems. In the second part of this paper, which is independent of any string configurations in $AdS_5\times S^5$ and concerns String Cosmology in $D=10$ dimensions. I will seriously argue that there was no Big Bang; I truly believe that the Universe has been there forever, see True Conclusions, Section 10.
|
hep-th/9901064
|
Ulrich Theis
|
Friedemann Brandt, Ulrich Theis
|
Supersymmetrization of generalized Freedman-Townsend models
|
4 pages. Talk given at the 32nd International Ahrenshoop Symposium on
the Theory of Elementary Particles in Buckow, Germany, Sep 1-5, 1998. To
appear in the Proceedings
|
Fortsch.Phys.48:41-44,2000
|
10.1002/(SICI)1521-3978(20001)48:1/3<41::AID-PROP41>3.0.CO;2-Z
|
ITP-UH-01/99
|
hep-th
| null |
We review briefly generalized Freedman-Townsend models found recently by
Henneaux and Knaepen, and provide supersymmetric versions of such models in
four dimensions which couple 2-form gauge potentials and ordinary gauge fields
in a gauge invariant and supersymmetric manner. The latter models have the
unusual feature that, in a WZ gauge, the supersymmetry transformations do not
commute with all the gauge transformations.
|
[
{
"created": "Fri, 15 Jan 1999 16:45:53 GMT",
"version": "v1"
}
] |
2017-04-26
|
[
[
"Brandt",
"Friedemann",
""
],
[
"Theis",
"Ulrich",
""
]
] |
We review briefly generalized Freedman-Townsend models found recently by Henneaux and Knaepen, and provide supersymmetric versions of such models in four dimensions which couple 2-form gauge potentials and ordinary gauge fields in a gauge invariant and supersymmetric manner. The latter models have the unusual feature that, in a WZ gauge, the supersymmetry transformations do not commute with all the gauge transformations.
|
hep-th/0503009
|
Swarnendu Sarkar
|
S. Sarkar, B. Sathiapalan
|
Aspects of Open-Closed Duality in a Background B-Field
|
33 pages, 4 figures, v2:references added, v3: minor changes, typos
corrected, references added
|
JHEP0505:062,2005
|
10.1088/1126-6708/2005/05/062
|
IMSC/2005/03/01
|
hep-th
| null |
We study closed string exchanges in background $B$-field. By analysing the
two point one loop amplitude in bosonic string theory, we show that tree-level
exchange of lowest lying, tachyonic and massless closed string modes, have IR
singularities similar to those of the nonplanar sector in noncommutative gauge
theories. We further isolate the contributions from each of the massless modes.
We interpret these results as the manifestation of open/closed string duality,
where the IR behaviour of the boundary noncommutative gauge theory is
reconstructed from the bulk theory of closed strings.
|
[
{
"created": "Tue, 1 Mar 2005 11:18:50 GMT",
"version": "v1"
},
{
"created": "Mon, 21 Mar 2005 08:44:41 GMT",
"version": "v2"
},
{
"created": "Mon, 20 Jun 2005 16:39:13 GMT",
"version": "v3"
},
{
"created": "Mon, 31 Oct 2005 11:16:15 GMT",
"version": "v4"
}
] |
2009-11-11
|
[
[
"Sarkar",
"S.",
""
],
[
"Sathiapalan",
"B.",
""
]
] |
We study closed string exchanges in background $B$-field. By analysing the two point one loop amplitude in bosonic string theory, we show that tree-level exchange of lowest lying, tachyonic and massless closed string modes, have IR singularities similar to those of the nonplanar sector in noncommutative gauge theories. We further isolate the contributions from each of the massless modes. We interpret these results as the manifestation of open/closed string duality, where the IR behaviour of the boundary noncommutative gauge theory is reconstructed from the bulk theory of closed strings.
|
1812.08611
|
Thomas Strobl
|
Alexei Kotov and Thomas Strobl
|
The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge
Theories
|
26 pages, 1 figure, addition of references and a new subsection
entitled "The gauge field sector of gauged maximal supergravity in d = 4".
Version accepted for publication in Comm. Math. Phys
| null |
10.1007/s00220-019-03569-3
| null |
hep-th math-ph math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We show that the data needed for the method of the embedding tensor employed
in gauging supergravity theories are precisely those of a Leibniz algebra (with
one of its induced quotient Lie algebras embedded into a rigid symmetry Lie
algebra that provides an additional "represtentation constraint"). Every
Leibniz algebra gives rise to a Lie n-algebra in a canonical way (for every
$n\in\mathbb{N}\cup \{ \infty \}$). It is the gauging of this
$L_\infty$-algebra that explains the tensor hierarchy of the bosonic sector of
gauged supergravity theories. The tower of p-from gauge fields corresponds to
Lyndon words of the universal enveloping algebra of the free Lie algebra of an
odd vector space in this construction. Truncation to some $n$ yields the
reduced field content needed in a concrete spacetime dimension.
|
[
{
"created": "Thu, 20 Dec 2018 14:43:56 GMT",
"version": "v1"
},
{
"created": "Fri, 21 Dec 2018 01:24:56 GMT",
"version": "v2"
},
{
"created": "Tue, 30 Jul 2019 16:43:52 GMT",
"version": "v3"
}
] |
2019-10-02
|
[
[
"Kotov",
"Alexei",
""
],
[
"Strobl",
"Thomas",
""
]
] |
We show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a Leibniz algebra (with one of its induced quotient Lie algebras embedded into a rigid symmetry Lie algebra that provides an additional "represtentation constraint"). Every Leibniz algebra gives rise to a Lie n-algebra in a canonical way (for every $n\in\mathbb{N}\cup \{ \infty \}$). It is the gauging of this $L_\infty$-algebra that explains the tensor hierarchy of the bosonic sector of gauged supergravity theories. The tower of p-from gauge fields corresponds to Lyndon words of the universal enveloping algebra of the free Lie algebra of an odd vector space in this construction. Truncation to some $n$ yields the reduced field content needed in a concrete spacetime dimension.
|
1805.04226
|
Sotaro Sugishita
|
Koji Hashimoto, Norihiro Iizuka, Sotaro Sugishita
|
Thoughts on Holographic Complexity and its Basis-dependence
|
7 pages
|
Phys. Rev. D 98, 046002 (2018)
|
10.1103/PhysRevD.98.046002
|
OU-HET-970
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
In this paper, we argue that holographic complexity should be a
basis-dependent quantity. Computational complexity of a state is defined as a
minimum number of gates required to obtain that state from the reference state.
Due to this minimality, it satisfies the triangle inequality, and can be
regarded as a (discrete version of) distance in the Hilbert space. However, we
show a no-go theorem that any basis-independent distance cannot reproduce the
behavior of the holographic complexity. Therefore, if holographic complexity is
dual to a distance in the Hilbert space, it should be basis-dependent, i.e., it
is not invariant under a change of the basis of the Hilbert space.
|
[
{
"created": "Fri, 11 May 2018 02:18:00 GMT",
"version": "v1"
}
] |
2018-08-15
|
[
[
"Hashimoto",
"Koji",
""
],
[
"Iizuka",
"Norihiro",
""
],
[
"Sugishita",
"Sotaro",
""
]
] |
In this paper, we argue that holographic complexity should be a basis-dependent quantity. Computational complexity of a state is defined as a minimum number of gates required to obtain that state from the reference state. Due to this minimality, it satisfies the triangle inequality, and can be regarded as a (discrete version of) distance in the Hilbert space. However, we show a no-go theorem that any basis-independent distance cannot reproduce the behavior of the holographic complexity. Therefore, if holographic complexity is dual to a distance in the Hilbert space, it should be basis-dependent, i.e., it is not invariant under a change of the basis of the Hilbert space.
|
0712.1254
|
Dimitri Skliros P
|
Dimitri Skliros and Mark Hindmarsh
|
Large Radius Hagedorn Regime in String Gas Cosmology
|
12 pages, 4 figures, more details presented in string thermodynamics
section, to be published in Physical Review D
|
Phys.Rev.D78:063539,2008
|
10.1103/PhysRevD.78.063539
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We calculate the equation of state of a gas of strings at high density in a
large toroidal universe, and use it to determine the cosmological evolution of
background metric and dilaton fields in the entire large radius Hagedorn
regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure
in this regime is not vanishing but of O(1), while the equation of state is
proportional to volume, which makes our solutions significantly different from
previously published approximate solutions. For example, we are able to
calculate the duration of the high-density "Hagedorn" phase, which increases
exponentially with increasing entropy, S. We go on to discuss the difficulties
of the scenario, quantifying the problems of establishing thermal equilibrium
and producing a large but not too weakly-coupled universe.
|
[
{
"created": "Sun, 9 Dec 2007 00:11:01 GMT",
"version": "v1"
},
{
"created": "Thu, 31 Jul 2008 23:06:54 GMT",
"version": "v2"
}
] |
2008-09-26
|
[
[
"Skliros",
"Dimitri",
""
],
[
"Hindmarsh",
"Mark",
""
]
] |
We calculate the equation of state of a gas of strings at high density in a large toroidal universe, and use it to determine the cosmological evolution of background metric and dilaton fields in the entire large radius Hagedorn regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure in this regime is not vanishing but of O(1), while the equation of state is proportional to volume, which makes our solutions significantly different from previously published approximate solutions. For example, we are able to calculate the duration of the high-density "Hagedorn" phase, which increases exponentially with increasing entropy, S. We go on to discuss the difficulties of the scenario, quantifying the problems of establishing thermal equilibrium and producing a large but not too weakly-coupled universe.
|
2208.02558
|
Vladimir Dzhunushaliev
|
Vladimir Dzhunushaliev, Vladimir Folomeev and Daulet Berkimbayev
|
Charge gap in SU(3) Yang-Mills-plus-nonlinear-spinor-field theory
|
6 pages, 3 figures
| null |
10.1140/epjc/s10052-023-11714-5
| null |
hep-th hep-ph
|
http://creativecommons.org/publicdomain/zero/1.0/
|
Particlelike solutions in SU(3) gauge Yang-Mills theory with color magnetic
and electric fields sourced by a nonlinear spinor field are obtained. The
asymptotic behavior of these fields is studied. It is shown that the electric
field exhibits the Coulomb asymptotic behavior, and one of the color components
of the magnetic field behaves asymptotically as the field of a magnetic dipole.
This allows one to determine the corresponding charge and magnetic moment. It
is shown that profiles of the color charge and magnetic moment have global
minima, which may be called charge and magnetic moment gaps. The relationship
between the total energy of the system and the color charge is obtained. The
physical reason for the appearance of the mass, charge, and magnetic moment
gaps in the theory under consideration is discussed.
|
[
{
"created": "Thu, 4 Aug 2022 10:00:08 GMT",
"version": "v1"
},
{
"created": "Fri, 16 Jun 2023 05:34:29 GMT",
"version": "v2"
}
] |
2023-07-26
|
[
[
"Dzhunushaliev",
"Vladimir",
""
],
[
"Folomeev",
"Vladimir",
""
],
[
"Berkimbayev",
"Daulet",
""
]
] |
Particlelike solutions in SU(3) gauge Yang-Mills theory with color magnetic and electric fields sourced by a nonlinear spinor field are obtained. The asymptotic behavior of these fields is studied. It is shown that the electric field exhibits the Coulomb asymptotic behavior, and one of the color components of the magnetic field behaves asymptotically as the field of a magnetic dipole. This allows one to determine the corresponding charge and magnetic moment. It is shown that profiles of the color charge and magnetic moment have global minima, which may be called charge and magnetic moment gaps. The relationship between the total energy of the system and the color charge is obtained. The physical reason for the appearance of the mass, charge, and magnetic moment gaps in the theory under consideration is discussed.
|
1902.04201
|
Andreas Gustavsson
|
Andreas Gustavsson
|
Abelian M5-brane on $S^6$
|
40 pages
| null |
10.1007/JHEP04(2019)140
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study the abelian M5 brane on $S^6$. From the spectrum we extract a series
expansion for the heat kernel. In particular we determine the normalization for
the coefficient $a$ in the M5 brane conformal anomaly. When we compare our
result with what one gets by computing the
Hadamard-Minakshisundaram-DeWitt-Seeley coefficients from local curvature
invariants on $S^6$, we first find a mismatch of one unit. This mismatch is due
to an overcounting of one zero mode. After subtracting this contribution, we
finally find agreement. We perform dimensional reduction along a singular
circle fiber to five dimensions where we find the conformal anomaly vanishes.
|
[
{
"created": "Tue, 12 Feb 2019 01:12:17 GMT",
"version": "v1"
},
{
"created": "Wed, 20 Feb 2019 00:47:53 GMT",
"version": "v2"
}
] |
2019-05-22
|
[
[
"Gustavsson",
"Andreas",
""
]
] |
We study the abelian M5 brane on $S^6$. From the spectrum we extract a series expansion for the heat kernel. In particular we determine the normalization for the coefficient $a$ in the M5 brane conformal anomaly. When we compare our result with what one gets by computing the Hadamard-Minakshisundaram-DeWitt-Seeley coefficients from local curvature invariants on $S^6$, we first find a mismatch of one unit. This mismatch is due to an overcounting of one zero mode. After subtracting this contribution, we finally find agreement. We perform dimensional reduction along a singular circle fiber to five dimensions where we find the conformal anomaly vanishes.
|
1806.00346
|
Dionisio Bazeia
|
D. Bazeia, L. Losano, Gonzalo J. Olmo
|
Novel connection between lump-like structures and quantum mechanics
|
8 pages, 12 figures. To appear in EPJP
|
Eur. Phys. J. Plus 133 (2018) 251
|
10.1140/epjp/i2018-12082-2
| null |
hep-th quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
This work deals with lump-like structures in models described by a single
real scalar field in two-dimensional spacetime. We start with a model that
supports lump-like configurations and use the deformation procedure to
construct scalar field theories that support both lumps and kinks, with the
corresponding stability investigation giving rise to new physical systems. Very
interestingly, we find models that support stable topological solutions, with
the stability potential being able to support a tower of non-negative bound
states, generating distinct families of potentials of current interest to
quantum mechanics. We also describe models where the lump-like solutions give
rise to stability potentials that have the shape of a double-well.
|
[
{
"created": "Fri, 1 Jun 2018 13:53:01 GMT",
"version": "v1"
}
] |
2018-07-06
|
[
[
"Bazeia",
"D.",
""
],
[
"Losano",
"L.",
""
],
[
"Olmo",
"Gonzalo J.",
""
]
] |
This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar field theories that support both lumps and kinks, with the corresponding stability investigation giving rise to new physical systems. Very interestingly, we find models that support stable topological solutions, with the stability potential being able to support a tower of non-negative bound states, generating distinct families of potentials of current interest to quantum mechanics. We also describe models where the lump-like solutions give rise to stability potentials that have the shape of a double-well.
|
1812.00947
|
Gaurav Narain
|
Gaurav Narain, Nirmalya Kajuri
|
Non-local scalar field on deSitter and its infrared behaviour
|
v2: few equations added, typos corrected, text added. version
accepted for publication in Physics Letters B
| null |
10.1016/j.physletb.2019.02.030
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We investigate free non-local massless and massive scalar field on deSitter
(dS) space-time. We compute the propagator for the non-local scalar field for
the corresponding theories on flat and deSitter space-times. It is seen that
for the non-local theory, the massless limit of massive propagator is smooth
for both flat and deSitter. Moreover, this limit matches exactly with the
massless propagator of the non-local scalar field for both flat and deSitter
space-time. The propagator is seen to respect dS invariance. Furthermore,
investigations of the non-local Green's function on deSitter for large
time-like separation shows that the propagator has no infrared divergences. The
dangerous infrared $\log$-divergent contributions which arise is local massless
theories are absent in the corresponding non-local version. Lack of infrared
divergences in the propagator hints at the strong role non-localities may play
in the dS infrared physics. This study suggest that non-locality can cure IR
issues in deSitter.
|
[
{
"created": "Mon, 3 Dec 2018 18:17:23 GMT",
"version": "v1"
},
{
"created": "Tue, 19 Feb 2019 14:46:08 GMT",
"version": "v2"
}
] |
2019-02-27
|
[
[
"Narain",
"Gaurav",
""
],
[
"Kajuri",
"Nirmalya",
""
]
] |
We investigate free non-local massless and massive scalar field on deSitter (dS) space-time. We compute the propagator for the non-local scalar field for the corresponding theories on flat and deSitter space-times. It is seen that for the non-local theory, the massless limit of massive propagator is smooth for both flat and deSitter. Moreover, this limit matches exactly with the massless propagator of the non-local scalar field for both flat and deSitter space-time. The propagator is seen to respect dS invariance. Furthermore, investigations of the non-local Green's function on deSitter for large time-like separation shows that the propagator has no infrared divergences. The dangerous infrared $\log$-divergent contributions which arise is local massless theories are absent in the corresponding non-local version. Lack of infrared divergences in the propagator hints at the strong role non-localities may play in the dS infrared physics. This study suggest that non-locality can cure IR issues in deSitter.
|
hep-th/0301039
|
Glenn Barnich
|
Glenn Barnich
|
Boundary charges in gauge theories: using Stokes theorem in the bulk
|
17 pages Latex file, improved presentation, main results unchanged,
additional section on first law, additional references
|
Class.Quant.Grav. 20 (2003) 3685-3698
|
10.1088/0264-9381/20/16/310
|
ULB-TH/03-01
|
hep-th gr-qc
| null |
Boundary charges in gauge theories (like the ADM mass in general relativity)
can be understood as integrals of linear conserved n-2 forms of the free theory
obtained by linearization around the background. These forms are associated
one-to-one to reducibility parameters of this background (like the time-like
Killing vector of Minkowski space-time). In this paper, closed n-2 forms in the
full interacting theory are constructed in terms of a one parameter family of
solutions to the full equations of motion that admits a reducibility parameter.
These forms thus allow one to apply Stokes theorem without bulk contributions
and, provided appropriate fall-off conditions are satisfied, they reduce
asymptotically near the boundary to the conserved n-2 forms of the linearized
theory. As an application, the first law of black hole mechanics in
asymptotically anti-de Sitter space-times is derived.
|
[
{
"created": "Tue, 7 Jan 2003 23:37:42 GMT",
"version": "v1"
},
{
"created": "Thu, 9 Jan 2003 17:10:25 GMT",
"version": "v2"
},
{
"created": "Wed, 16 Apr 2003 19:54:33 GMT",
"version": "v3"
}
] |
2009-11-10
|
[
[
"Barnich",
"Glenn",
""
]
] |
Boundary charges in gauge theories (like the ADM mass in general relativity) can be understood as integrals of linear conserved n-2 forms of the free theory obtained by linearization around the background. These forms are associated one-to-one to reducibility parameters of this background (like the time-like Killing vector of Minkowski space-time). In this paper, closed n-2 forms in the full interacting theory are constructed in terms of a one parameter family of solutions to the full equations of motion that admits a reducibility parameter. These forms thus allow one to apply Stokes theorem without bulk contributions and, provided appropriate fall-off conditions are satisfied, they reduce asymptotically near the boundary to the conserved n-2 forms of the linearized theory. As an application, the first law of black hole mechanics in asymptotically anti-de Sitter space-times is derived.
|
hep-th/9612103
| null |
M.C. Diamantini (CERN), F. Quevedo (CERN) and C.A.Trugenberger
(University of Geneva)
|
Confining String with Topological Term
|
11 pages, harvmac
|
Phys.Lett. B396 (1997) 115-121
|
10.1016/S0370-2693(97)00132-9
|
CERN-TH/96-319, UGVA-DPT 1996/10-995
|
hep-th
| null |
We consider several aspects of `confining strings', recently proposed to
describe the confining phase of gauge field theories.
We perform the exact duality transformation that leads to the confining
string action and show that it reduces to the Polyakov action in the
semiclassical approximation. In 4D we introduce a `$\theta$-term' and compute
the low-energy effective action for the confining string in a derivative
expansion. We find that the coefficient of the extrinsic curvature (stiffness)
is negative, confirming previous proposals. In the absence of a $\theta$-term,
the effective string action is only a cut-off theory for finite values of the
coupling e, whereas for generic values of $\theta$, the action can be
renormalized and to leading order we obtain the Nambu-Goto action plus a
topological `spin' term that could stabilize the system.
|
[
{
"created": "Tue, 10 Dec 1996 14:59:31 GMT",
"version": "v1"
}
] |
2016-09-06
|
[
[
"Diamantini",
"M. C.",
"",
"CERN"
],
[
"Quevedo",
"F.",
"",
"CERN"
],
[
"Trugenberger",
"C. A.",
"",
"University of Geneva"
]
] |
We consider several aspects of `confining strings', recently proposed to describe the confining phase of gauge field theories. We perform the exact duality transformation that leads to the confining string action and show that it reduces to the Polyakov action in the semiclassical approximation. In 4D we introduce a `$\theta$-term' and compute the low-energy effective action for the confining string in a derivative expansion. We find that the coefficient of the extrinsic curvature (stiffness) is negative, confirming previous proposals. In the absence of a $\theta$-term, the effective string action is only a cut-off theory for finite values of the coupling e, whereas for generic values of $\theta$, the action can be renormalized and to leading order we obtain the Nambu-Goto action plus a topological `spin' term that could stabilize the system.
|
hep-th/0209128
|
Changhyun Ahn
|
Changhyun Ahn and Kyungsung Woo
|
Domain Wall from Gauged d=4, N=8 Supergravity: Part II
|
34 pp;corrected the discussions on the critical points in the reduced
parameter space in sections 5 and 6;to appear in JHEP
|
JHEP 0311 (2003) 014
|
10.1088/1126-6708/2003/11/014
| null |
hep-th
| null |
The scalar potentials of the non-semi-simple CSO(p,8-p)(p=7,6,5) gaugings of
N=8 supergravity are studied for critical points. The CSO(7,1) gauging has no
G_2-invariant critical points, the CSO(6,2) gauging has three new
SU(3)-invariant AdS critical points and the CSO(5,3) gauging has no
SO(5)-invariant critical points. The scalar potential of CSO(6,2) gauging in
four dimensions we discovered provides the SU(3) invariant scalar potential of
five dimensional SO(6) gauged supergravity. The nontrivial effective scalar
potential can be written in terms of the superpotential which can be read off
from A_1 tensor of the theory. We discuss first-order domain wall solutions by
analyzing the supergravity scalar-gravity action and using some algebraic
relations in a complex eigenvalue of A_1 tensor. We examine domain wall
solutions of G_2 sectors of noncompact SO(7,1) and CSO(7,1) gaugings and SU(3)
sectors of SO(6,2) and CSO(6,2) gaugings. They share common features with each
sector of compact SO(8) gauged N=8 supergravity in four dimensions. We analyze
the scalar potentials of the CSO(p,q,8-p-q) gauged supergravity we have found
before. The CSO(p,6-p,2) gauge theory in four dimensions can be reduced from
the SO(p,6-p) gauge theory in five dimensions. Moreover, the SO(p,5-p) gauge
theory in seven dimensions reduces to CSO(p,5-p,3) gauge theory in four
dimensions. Similarly, CSO(p,q-p,8-q) gauge theories in four dimensions are
related to SO(p,q-p)(q=2,3,4,7) gauge theories in other dimensions.
|
[
{
"created": "Mon, 16 Sep 2002 12:00:49 GMT",
"version": "v1"
},
{
"created": "Thu, 14 Aug 2003 02:40:23 GMT",
"version": "v2"
},
{
"created": "Mon, 10 Nov 2003 12:12:20 GMT",
"version": "v3"
}
] |
2009-11-07
|
[
[
"Ahn",
"Changhyun",
""
],
[
"Woo",
"Kyungsung",
""
]
] |
The scalar potentials of the non-semi-simple CSO(p,8-p)(p=7,6,5) gaugings of N=8 supergravity are studied for critical points. The CSO(7,1) gauging has no G_2-invariant critical points, the CSO(6,2) gauging has three new SU(3)-invariant AdS critical points and the CSO(5,3) gauging has no SO(5)-invariant critical points. The scalar potential of CSO(6,2) gauging in four dimensions we discovered provides the SU(3) invariant scalar potential of five dimensional SO(6) gauged supergravity. The nontrivial effective scalar potential can be written in terms of the superpotential which can be read off from A_1 tensor of the theory. We discuss first-order domain wall solutions by analyzing the supergravity scalar-gravity action and using some algebraic relations in a complex eigenvalue of A_1 tensor. We examine domain wall solutions of G_2 sectors of noncompact SO(7,1) and CSO(7,1) gaugings and SU(3) sectors of SO(6,2) and CSO(6,2) gaugings. They share common features with each sector of compact SO(8) gauged N=8 supergravity in four dimensions. We analyze the scalar potentials of the CSO(p,q,8-p-q) gauged supergravity we have found before. The CSO(p,6-p,2) gauge theory in four dimensions can be reduced from the SO(p,6-p) gauge theory in five dimensions. Moreover, the SO(p,5-p) gauge theory in seven dimensions reduces to CSO(p,5-p,3) gauge theory in four dimensions. Similarly, CSO(p,q-p,8-q) gauge theories in four dimensions are related to SO(p,q-p)(q=2,3,4,7) gauge theories in other dimensions.
|
1811.02369
|
Shota Komatsu
|
Simone Giombi, Shota Komatsu
|
More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE,
Nonplanar Corrections and Quantum Spectral Curve
|
44 pages + appendices. v2 references added
| null |
10.1088/1751-8121/ab046c
|
PUTP-2572
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We perform exact computations of correlation functions of 1/2-BPS local
operators and protected operator insertions on the 1/8-BPS Wilson loop in
$\mathcal{N}=4$ SYM. This generalizes the results of our previous paper
arXiv:1802.05201, which employs supersymmetric localization, OPE and the
Gram-Schmidt process. In particular, we conduct a detailed analysis for the
1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines
an interesting nontrivial defect CFT. We compute its bulk-defect structure
constants at finite 't Hooft coupling, and present simple integral expressions
in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a
formalism originally introduced for the computation of the operator spectrum.
The results at strong coupling are found to be in precise agreement with the
holographic calculation based on perturbation theory around the AdS$_2$ string
worldsheet, where they correspond to correlation functions of open string
fluctuations and closed string vertex operators inserted on the worldsheet.
Along the way, we clarify several aspects of the Gram-Schmidt analysis which
were not addressed in the previous paper. In particular, we clarify the role
played by the multi-trace operators at the non-planar level, and confirm its
importance by computing the non-planar correction to the defect two-point
function. We also provide a formula for the first non-planar correction to the
defect correlators in terms of the Quantum Spectral Curve, which suggests the
potential applicability of the formalism to the non-planar correlation
functions.
|
[
{
"created": "Tue, 6 Nov 2018 14:35:33 GMT",
"version": "v1"
},
{
"created": "Fri, 16 Nov 2018 04:00:36 GMT",
"version": "v2"
}
] |
2019-05-22
|
[
[
"Giombi",
"Simone",
""
],
[
"Komatsu",
"Shota",
""
]
] |
We perform exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $\mathcal{N}=4$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite 't Hooft coupling, and present simple integral expressions in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$_2$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. In particular, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.
|
1103.5587
|
Matt Visser
|
Matt Visser (Victoria University of Wellington)
|
Status of Horava gravity: A personal perspective
|
V1: 11 pages. Based on a talk at the ERE2010 conference, Granada,
Spain, September 2010. V2: three references added
|
J.Phys.Conf.Ser. 314 (2011) 012002
|
10.1088/1742-6596/314/1/012002
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Horava gravity is a relatively recent (Jan 2009) idea in theoretical physics
for trying to develop a quantum field theory of gravity. It is not a string
theory, nor loop quantum gravity, but is instead a traditional quantum field
theory that breaks Lorentz invariance at ultra-high (presumably
trans-Planckian) energies, while retaining approximate Lorentz invariance at
low and medium (sub-Planckian) energies. The challenge is to keep the Lorentz
symmetry breaking controlled and small - small enough to be compatible with
experiment. I will give a very general overview of what is going on in this
field, paying particular attention to the disturbing role of the scalar
graviton.
|
[
{
"created": "Tue, 29 Mar 2011 10:09:22 GMT",
"version": "v1"
},
{
"created": "Mon, 4 Apr 2011 00:25:23 GMT",
"version": "v2"
}
] |
2017-11-29
|
[
[
"Visser",
"Matt",
"",
"Victoria University of Wellington"
]
] |
Horava gravity is a relatively recent (Jan 2009) idea in theoretical physics for trying to develop a quantum field theory of gravity. It is not a string theory, nor loop quantum gravity, but is instead a traditional quantum field theory that breaks Lorentz invariance at ultra-high (presumably trans-Planckian) energies, while retaining approximate Lorentz invariance at low and medium (sub-Planckian) energies. The challenge is to keep the Lorentz symmetry breaking controlled and small - small enough to be compatible with experiment. I will give a very general overview of what is going on in this field, paying particular attention to the disturbing role of the scalar graviton.
|
1706.00016
|
Daniel Brattan K
|
Daniel K. Brattan, Omrie Ovdat and Eric Akkermans
|
Scale anomaly of a Lifshitz scalar: a universal quantum phase transition
to discrete scale invariance
|
6 pages, 3 figures + 3 pages supplementary material; v2: minor typos
corrected, additional text of published version added
|
Phys. Rev. D 97, 061701 (2018)
|
10.1103/PhysRevD.97.061701
|
USTC-ICTS-17-08
|
hep-th cond-mat.mes-hall math-ph math.MP quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We demonstrate the existence of a universal transition from a continuous
scale invariant phase to a discrete scale invariant phase for a class of
one-dimensional quantum systems with anisotropic scaling symmetry between space
and time. These systems describe a Lifshitz scalar interacting with a
background potential. The transition occurs at a critical coupling
$\lambda_{c}$ corresponding to a strongly attractive potential.
|
[
{
"created": "Wed, 31 May 2017 18:00:02 GMT",
"version": "v1"
},
{
"created": "Sat, 21 Apr 2018 12:45:28 GMT",
"version": "v2"
}
] |
2018-04-24
|
[
[
"Brattan",
"Daniel K.",
""
],
[
"Ovdat",
"Omrie",
""
],
[
"Akkermans",
"Eric",
""
]
] |
We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time. These systems describe a Lifshitz scalar interacting with a background potential. The transition occurs at a critical coupling $\lambda_{c}$ corresponding to a strongly attractive potential.
|
2304.10102
|
Ankit Aggarwal
|
Ankit Aggarwal, Alejandra Castro, St\'ephane Detournay and Beatrix
M\"uhlmann
|
Near-Extremal Limits of Warped Black Holes
|
43 pages, v2: minor typos corrected, reference added
|
SciPost Phys. 15, 083 (2023)
|
10.21468/SciPostPhys.15.3.083
| null |
hep-th
|
http://creativecommons.org/licenses/by/4.0/
|
A holographic description of three-dimensional warped black holes suffers
from ambiguities due to a seemingly harmless choice of coordinate system. This
gives rise to the notion of ensembles in warped black holes, and we focus on
two of them: the canonical and quadratic ensemble. Our aim is to quantify the
imprint of these ensembles in the near-extremal limit of a warped black hole.
To this end, for each ensemble, we explore the thermodynamic response and
evaluate greybody factors. We also set-up a holographic dictionary in their
near-AdS$_2$ region, and decode aspects of the dual near-CFT$_1$. This gives us
different perspectives of the black hole that we can contrast and compare. On
the one hand, we find perfect agreement between the near-extremal limit of the
canonical ensemble warped black holes, their near-AdS$_2$ effective analysis,
and a warped conformal field theory description. On the other, we are led to
rule out the quadratic ensemble due to inconsistencies at the quantum level
with the near-AdS$_2$ effective description.
|
[
{
"created": "Thu, 20 Apr 2023 06:07:38 GMT",
"version": "v1"
},
{
"created": "Mon, 10 Jul 2023 21:35:36 GMT",
"version": "v2"
}
] |
2023-09-06
|
[
[
"Aggarwal",
"Ankit",
""
],
[
"Castro",
"Alejandra",
""
],
[
"Detournay",
"Stéphane",
""
],
[
"Mühlmann",
"Beatrix",
""
]
] |
A holographic description of three-dimensional warped black holes suffers from ambiguities due to a seemingly harmless choice of coordinate system. This gives rise to the notion of ensembles in warped black holes, and we focus on two of them: the canonical and quadratic ensemble. Our aim is to quantify the imprint of these ensembles in the near-extremal limit of a warped black hole. To this end, for each ensemble, we explore the thermodynamic response and evaluate greybody factors. We also set-up a holographic dictionary in their near-AdS$_2$ region, and decode aspects of the dual near-CFT$_1$. This gives us different perspectives of the black hole that we can contrast and compare. On the one hand, we find perfect agreement between the near-extremal limit of the canonical ensemble warped black holes, their near-AdS$_2$ effective analysis, and a warped conformal field theory description. On the other, we are led to rule out the quadratic ensemble due to inconsistencies at the quantum level with the near-AdS$_2$ effective description.
|
hep-th/9709102
|
Stefan Mashkevich
|
Stefan Mashkevich (ITP, Kiev)
|
Chern-Simons Field Theory and Generalizations of Anyons
|
6 pages, LATEX. Contributed paper at the International Europhysics
Conference on High Energy Physics HEP-97 (Jerusalem, Israel, 19--26 August
1997)
| null | null | null |
hep-th
| null |
It is well known that charges coupled to a pure Chern-Simons gauge field in
(2+1) dimensions undergo an effective change of statistics, i.e., become
anyons. We will consider several generalizations thereof, arising when the
gauge field is more general. The first one is ``multispecies anyons''---charged
particles of several species coupled to one, or possibly several, Chern-Simons
fields. The second one is finite-size anyons, which are charged particles
coupled to a gauge field described by the Chern-Simons term plus some other
term. In fact, rigorously speaking, quasielectrons and quasiholes in the
fractional quantum Hall effect are multispecies finite-size anyons. The third
one is an analog of finite-size anyons which arises in a model with a mixed
Chern-Simons term; notably, this model is P,T-invariant, which opens the way
for practical applications even when there is no parity-breaking magnetic
field.
|
[
{
"created": "Mon, 15 Sep 1997 16:20:55 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Mashkevich",
"Stefan",
"",
"ITP, Kiev"
]
] |
It is well known that charges coupled to a pure Chern-Simons gauge field in (2+1) dimensions undergo an effective change of statistics, i.e., become anyons. We will consider several generalizations thereof, arising when the gauge field is more general. The first one is ``multispecies anyons''---charged particles of several species coupled to one, or possibly several, Chern-Simons fields. The second one is finite-size anyons, which are charged particles coupled to a gauge field described by the Chern-Simons term plus some other term. In fact, rigorously speaking, quasielectrons and quasiholes in the fractional quantum Hall effect are multispecies finite-size anyons. The third one is an analog of finite-size anyons which arises in a model with a mixed Chern-Simons term; notably, this model is P,T-invariant, which opens the way for practical applications even when there is no parity-breaking magnetic field.
|
0710.5480
|
Lorenzo Cornalba
|
Lorenzo Cornalba
|
Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
|
25 pages, 6 figures, added references and minor mistakes corrected
| null | null | null |
hep-th hep-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We analyze conformal field theory 4-point functions of the form A ~ O_1(x_1)
O_2(x_2) O_1(x_3) O_2(x_4), where the operators O_i are scalar primaries. We
show that, in the Lorentzian regime, the limit x_1 -> x_3 is dominated by the
exchange of conformal partial waves of highest spin. When partial waves of
arbitrary spin contribute to A, the behavior of the Lorentzian amplitude for
x_1 -> x_3 must be analyzed using complex-spin techniques, leading to a
generalized Regge theory for CFT's. Whenever the CFT is dual to a string
theory, the string tree-level contribution A_tree to the amplitude A presents a
Regge pole corresponding the a gravi-reggeon exchange. In this case, we apply
the impact parameter representation for CFT amplitudes, previously developed,
to analyze multiple reggeon exchanges in the eikonal limit. As an example, we
apply these general techniques to N=4 super-Yang-Mills theory in d=4 in the
limit of large 't Hooft coupling, including the leading string corrections to
pure graviton exchange.
|
[
{
"created": "Mon, 29 Oct 2007 16:52:27 GMT",
"version": "v1"
},
{
"created": "Fri, 28 Dec 2007 08:58:15 GMT",
"version": "v2"
},
{
"created": "Mon, 6 Oct 2008 15:35:23 GMT",
"version": "v3"
}
] |
2008-10-06
|
[
[
"Cornalba",
"Lorenzo",
""
]
] |
We analyze conformal field theory 4-point functions of the form A ~ O_1(x_1) O_2(x_2) O_1(x_3) O_2(x_4), where the operators O_i are scalar primaries. We show that, in the Lorentzian regime, the limit x_1 -> x_3 is dominated by the exchange of conformal partial waves of highest spin. When partial waves of arbitrary spin contribute to A, the behavior of the Lorentzian amplitude for x_1 -> x_3 must be analyzed using complex-spin techniques, leading to a generalized Regge theory for CFT's. Whenever the CFT is dual to a string theory, the string tree-level contribution A_tree to the amplitude A presents a Regge pole corresponding the a gravi-reggeon exchange. In this case, we apply the impact parameter representation for CFT amplitudes, previously developed, to analyze multiple reggeon exchanges in the eikonal limit. As an example, we apply these general techniques to N=4 super-Yang-Mills theory in d=4 in the limit of large 't Hooft coupling, including the leading string corrections to pure graviton exchange.
|
hep-th/0601231
|
Adel Bilal
|
Adel Bilal and Steffen Metzger
|
Relating prepotentials and quantum vacua of N=1 gauge theories with
different tree-level superpotentials
|
27 pages, 10 figures, modified version to appear in JHEP, discussion
of the physical meaning of the Z_k symmetry added
|
JHEP0606:004,2006
|
10.1088/1126-6708/2006/06/004
|
LPTENS-06/02, LMU-ASC06/06
|
hep-th
| null |
We consider N=1 supersymmetric U(N) gauge theories with Z_k symmetric
tree-level superpotentials W for an adjoint chiral multiplet. We show that (for
integer 2N/k) this Z_k symmetry survives in the quantum effective theory as a
corresponding symmetry of the effective superpotential W_eff(S_i) under
permutations of the S_i. For W(x)=^W(h(x)) with h(x)=x^k, this allows us to
express the prepotential F_0 and effective superpotential W_eff on certain
submanifolds of the moduli space in terms of an ^F_0 and ^W_eff of a different
theory with tree-level superpotential ^W. In particular, if the Z_k symmetric
polynomial W(x) is of degree 2k, then ^W is gaussian and we obtain very
explicit formulae for F_0 and W_eff. Moreover, in this case, every vacuum of
the effective Veneziano-Yankielowicz superpotential ^W_eff is shown to give
rise to a vacuum of W_eff. Somewhat surprisingly, at the level of the
prepotential F_0(S_i) the permutation symmetry only holds for k=2, while it is
anomalous for k>2 due to subtleties related to the non-compact period
integrals. Some of these results are also extended to general polynomial
relations h(x) between the tree-level superpotentials.
|
[
{
"created": "Tue, 31 Jan 2006 11:48:25 GMT",
"version": "v1"
},
{
"created": "Wed, 1 Feb 2006 12:23:45 GMT",
"version": "v2"
},
{
"created": "Tue, 30 May 2006 11:33:45 GMT",
"version": "v3"
}
] |
2009-11-11
|
[
[
"Bilal",
"Adel",
""
],
[
"Metzger",
"Steffen",
""
]
] |
We consider N=1 supersymmetric U(N) gauge theories with Z_k symmetric tree-level superpotentials W for an adjoint chiral multiplet. We show that (for integer 2N/k) this Z_k symmetry survives in the quantum effective theory as a corresponding symmetry of the effective superpotential W_eff(S_i) under permutations of the S_i. For W(x)=^W(h(x)) with h(x)=x^k, this allows us to express the prepotential F_0 and effective superpotential W_eff on certain submanifolds of the moduli space in terms of an ^F_0 and ^W_eff of a different theory with tree-level superpotential ^W. In particular, if the Z_k symmetric polynomial W(x) is of degree 2k, then ^W is gaussian and we obtain very explicit formulae for F_0 and W_eff. Moreover, in this case, every vacuum of the effective Veneziano-Yankielowicz superpotential ^W_eff is shown to give rise to a vacuum of W_eff. Somewhat surprisingly, at the level of the prepotential F_0(S_i) the permutation symmetry only holds for k=2, while it is anomalous for k>2 due to subtleties related to the non-compact period integrals. Some of these results are also extended to general polynomial relations h(x) between the tree-level superpotentials.
|
1706.09034
|
Michael Fuchs
|
Ralph Blumenhagen, Michael Fuchs, Matthias Traube
|
On the Structure of Quantum L$_\infty$ algebras
|
21 pages, v2: clarifications, version published in JHEP
| null | null |
MPP-2017-126
|
hep-th math-ph math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
It is believed that any classical gauge symmetry gives rise to an L$_\infty$
algebra. Based on the recently realized relation between classical ${\cal W}$
algebras and L$_\infty$ algebras, we analyze how this generalizes to the
quantum case. Guided by the existence of quantum ${\cal W}$ algebras, we
provide a physically well motivated definition of quantum L$_\infty$ algebras
describing the consistency of global symmetries in quantum field theories. In
this case we are restricted to only two non-trivial graded vector spaces $X_0$
and $X_{-1}$ containing the symmetry variations and the symmetry generators.
This quantum L$_\infty$ algebra structure is explicitly exemplified for the
quantum ${\cal W}_3$ algebra. The natural quantum product between fields is the
normal ordered one so that, due to contractions between quantum fields, the
higher L$_\infty$ relations receive off-diagonal quantum corrections.
Curiously, these are not present in the loop L$_\infty$ algebra of closed
string field theory.
|
[
{
"created": "Tue, 27 Jun 2017 20:06:14 GMT",
"version": "v1"
},
{
"created": "Wed, 25 Oct 2017 12:20:14 GMT",
"version": "v2"
}
] |
2017-10-26
|
[
[
"Blumenhagen",
"Ralph",
""
],
[
"Fuchs",
"Michael",
""
],
[
"Traube",
"Matthias",
""
]
] |
It is believed that any classical gauge symmetry gives rise to an L$_\infty$ algebra. Based on the recently realized relation between classical ${\cal W}$ algebras and L$_\infty$ algebras, we analyze how this generalizes to the quantum case. Guided by the existence of quantum ${\cal W}$ algebras, we provide a physically well motivated definition of quantum L$_\infty$ algebras describing the consistency of global symmetries in quantum field theories. In this case we are restricted to only two non-trivial graded vector spaces $X_0$ and $X_{-1}$ containing the symmetry variations and the symmetry generators. This quantum L$_\infty$ algebra structure is explicitly exemplified for the quantum ${\cal W}_3$ algebra. The natural quantum product between fields is the normal ordered one so that, due to contractions between quantum fields, the higher L$_\infty$ relations receive off-diagonal quantum corrections. Curiously, these are not present in the loop L$_\infty$ algebra of closed string field theory.
|
hep-th/0502217
|
Nora Breton
|
Nora Breton
|
Stability of nonlinear magnetic black holes
|
7 pages, submitted to Phys. Rev. D.In this version the stability of
the solitonic solutions is addressed
|
Phys.Rev. D72 (2005) 044015
|
10.1103/PhysRevD.72.044015
| null |
hep-th
| null |
We study the stability of static spherically symmetric exact solutions of
Einstein equations coupled with nonlinear electrodynamics, in the magnetic
sector. These solutions satisfy the heuristic model proposed by
Ashtekar-Corichi-Sudarsky for hairy black holes, meaning that the horizon mass
is related to their Arnowitt-Deser-Misner (ADM) mass and to the corresponding
particle-like solution. We test the unstability conjecture that emerges for
hairy black holes and it turned out that it becomes confirmed except for the
Einstein-Born-Infeld solutions.
|
[
{
"created": "Thu, 24 Feb 2005 14:16:58 GMT",
"version": "v1"
},
{
"created": "Wed, 25 May 2005 15:00:57 GMT",
"version": "v2"
}
] |
2009-11-11
|
[
[
"Breton",
"Nora",
""
]
] |
We study the stability of static spherically symmetric exact solutions of Einstein equations coupled with nonlinear electrodynamics, in the magnetic sector. These solutions satisfy the heuristic model proposed by Ashtekar-Corichi-Sudarsky for hairy black holes, meaning that the horizon mass is related to their Arnowitt-Deser-Misner (ADM) mass and to the corresponding particle-like solution. We test the unstability conjecture that emerges for hairy black holes and it turned out that it becomes confirmed except for the Einstein-Born-Infeld solutions.
|
hep-th/9305131
|
Subir Sachdev
|
Subir Sachdev
|
Polylogarithm Identities in a Conformal Field Theory in Three Dimensions
|
LATEX, 7 pages
|
Phys.Lett. B309 (1993) 285-288
|
10.1016/0370-2693(93)90935-B
| null |
hep-th cond-mat
| null |
The $N=\infty$ vector $O(N)$ model is a solvable, interacting field theory in
three dimensions ($D$). In a recent paper with A. Chubukov and J.
Ye~\cite{self}, we have computed a universal number, $\tilde{c}$,
characterizing the size dependence of the free energy at the
conformally-invariant critical point of this theory. The result~\cite{self} for
$\tilde{c}$ can be expressed in terms of polylogarithms. Here, we use
non-trivial polylogarithm identities to show that $\tilde{c}/N = 4/5$, a
rational number; this result is curiously parallel to recent work on
dilogarithm identities in $D=2$ conformal theories. The amplitude of the
stress-stress correlator of this theory, $c$ (which is the analog of the
central charge), is determined to be $c/N=3/4$, also rational. Unitary
conformal theories in $D=2$ always have $c = \tilde{c}$; thus such a result is
clearly not valid in $D=3$.
|
[
{
"created": "Tue, 25 May 1993 06:47:12 GMT",
"version": "v1"
}
] |
2009-10-22
|
[
[
"Sachdev",
"Subir",
""
]
] |
The $N=\infty$ vector $O(N)$ model is a solvable, interacting field theory in three dimensions ($D$). In a recent paper with A. Chubukov and J. Ye~\cite{self}, we have computed a universal number, $\tilde{c}$, characterizing the size dependence of the free energy at the conformally-invariant critical point of this theory. The result~\cite{self} for $\tilde{c}$ can be expressed in terms of polylogarithms. Here, we use non-trivial polylogarithm identities to show that $\tilde{c}/N = 4/5$, a rational number; this result is curiously parallel to recent work on dilogarithm identities in $D=2$ conformal theories. The amplitude of the stress-stress correlator of this theory, $c$ (which is the analog of the central charge), is determined to be $c/N=3/4$, also rational. Unitary conformal theories in $D=2$ always have $c = \tilde{c}$; thus such a result is clearly not valid in $D=3$.
|
1909.04682
|
Matteo Bertolini
|
Riccardo Argurio, Matteo Bertolini, Shani Meynet, Antoine Pasternak
|
On supersymmetry breaking vacua from D-branes at orientifold
singularities
|
50 pages, several figures. v2: minor edits, version to appear in
journal. v3: typos corrected
| null |
10.1007/JHEP12(2019)145
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We present a large class of models of D-branes at (orientifold) Calabi-Yau
singularities which enjoy dynamical supersymmetry breaking at low energy, by
means of either the $SU(5)$ or 3-2 supersymmetry breaking models. Once embedded
in a warped throat or, equivalently, in a large $N$ theory, all models display
an instability along a Coulomb branch direction towards supersymmetry
preserving vacua. Interestingly, the nature of the runaway mechanism is
model-independent and has a precise geometrical interpretation. This naturally
suggests the properties a Calabi-Yau singularity should have in order for such
instability not to occur.
|
[
{
"created": "Tue, 10 Sep 2019 18:00:08 GMT",
"version": "v1"
},
{
"created": "Thu, 19 Dec 2019 09:50:01 GMT",
"version": "v2"
},
{
"created": "Fri, 7 Feb 2020 10:30:42 GMT",
"version": "v3"
}
] |
2020-02-10
|
[
[
"Argurio",
"Riccardo",
""
],
[
"Bertolini",
"Matteo",
""
],
[
"Meynet",
"Shani",
""
],
[
"Pasternak",
"Antoine",
""
]
] |
We present a large class of models of D-branes at (orientifold) Calabi-Yau singularities which enjoy dynamical supersymmetry breaking at low energy, by means of either the $SU(5)$ or 3-2 supersymmetry breaking models. Once embedded in a warped throat or, equivalently, in a large $N$ theory, all models display an instability along a Coulomb branch direction towards supersymmetry preserving vacua. Interestingly, the nature of the runaway mechanism is model-independent and has a precise geometrical interpretation. This naturally suggests the properties a Calabi-Yau singularity should have in order for such instability not to occur.
|
1104.5490
|
Jurgis Pasukonis
|
Amihay Hanany, Yang-Hui He, Vishnu Jejjala, Jurgis Pasukonis, Sanjaye
Ramgoolam, Diego Rodriguez-Gomez
|
The Beta Ansatz: A Tale of Two Complex Structures
|
36 pages, 8 figures
|
JHEP 1106:056,2011
|
10.1007/JHEP06(2011)056
| null |
hep-th math-ph math.AG math.MP math.NT
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Brane tilings, sometimes called dimer models, are a class of bipartite graphs
on a torus which encode the gauge theory data of four-dimensional SCFTs dual to
D3-branes probing toric Calabi--Yau threefolds. An efficient way of encoding
this information exploits the theory of dessin d'enfants, expressing the
structure in terms of a permutation triple, which is in turn related to a Belyi
pair, namely a holomorphic map from a torus to a P^1 with three marked points.
The procedure of a-maximization, in the context of isoradial embeddings of the
dimer, also associates a complex structure to the torus, determined by the
R-charges in the SCFT, which can be compared with the Belyi complex structure.
Algorithms for the explicit construction of the Belyi pairs are described in
detail. In the case of orbifolds, these algorithms are related to the
construction of covers of elliptic curves, which exploits the properties of
Weierstrass elliptic functions. We present a counterexample to a previous
conjecture identifying the complex structure of the Belyi curve to the complex
structure associated with R-charges.
|
[
{
"created": "Thu, 28 Apr 2011 19:58:22 GMT",
"version": "v1"
}
] |
2011-06-20
|
[
[
"Hanany",
"Amihay",
""
],
[
"He",
"Yang-Hui",
""
],
[
"Jejjala",
"Vishnu",
""
],
[
"Pasukonis",
"Jurgis",
""
],
[
"Ramgoolam",
"Sanjaye",
""
],
[
"Rodriguez-Gomez",
"Diego",
""
]
] |
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi--Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d'enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P^1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstrass elliptic functions. We present a counterexample to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges.
|
1508.01957
|
Alexei Morozov
|
A.Morozov, An.Morozov, A.Popolitov
|
Matrix model and dimensions at hypercube vertices
|
37 pages
|
Theoretical and Mathematical Physics, 192 (1) (2017) 1039-1079
|
10.1134/S004057791707008X
|
IITP/TH-09/15
|
hep-th math-ph math.GT math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
In hypercube approach to correlation functions in Chern-Simons theory (knot
polynomials) the central role is played by the numbers of cycles, in which the
link diagram is decomposed under different resolutions. Certain functions of
these numbers are further interpreted as dimensions of graded spaces,
associated with hypercube vertices. Finding these functions is, however, a
somewhat non-trivial problem. In arXiv:1506.07516 it was suggested to solve it
with the help of the matrix model technique, in the spirit of AMM/EO
topological recursion. In this paper we further elaborate on this idea and
provide a vast collection of non-trivial examples, related both to ordinary and
virtual links and knots. Remarkably, most powerful versions of the formalism
freely convert ordinary knots/links to virtual and back -- moreover, go beyond
the knot-related set of the (2,2)-valent graphs.
|
[
{
"created": "Sat, 8 Aug 2015 21:34:15 GMT",
"version": "v1"
}
] |
2017-07-20
|
[
[
"Morozov",
"A.",
""
],
[
"Morozov",
"An.",
""
],
[
"Popolitov",
"A.",
""
]
] |
In hypercube approach to correlation functions in Chern-Simons theory (knot polynomials) the central role is played by the numbers of cycles, in which the link diagram is decomposed under different resolutions. Certain functions of these numbers are further interpreted as dimensions of graded spaces, associated with hypercube vertices. Finding these functions is, however, a somewhat non-trivial problem. In arXiv:1506.07516 it was suggested to solve it with the help of the matrix model technique, in the spirit of AMM/EO topological recursion. In this paper we further elaborate on this idea and provide a vast collection of non-trivial examples, related both to ordinary and virtual links and knots. Remarkably, most powerful versions of the formalism freely convert ordinary knots/links to virtual and back -- moreover, go beyond the knot-related set of the (2,2)-valent graphs.
|
1410.6360
|
Ahmet Emir Gumrukcuoglu
|
Mattia Colombo, A. Emir Gumrukcuoglu, Thomas P. Sotiriou
|
Horava gravity with mixed derivative terms
|
9 pages
| null |
10.1103/PhysRevD.91.044021
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Horava gravity has been constructed so as to exhibit anisotropic scaling in
the ultraviolet, as this renders the theory power-counting renormalizable.
However, when coupled to matter, the theory has been shown to suffer from
quadratic divergences. A way to cure these divergences is to add terms with
both time and space derivatives. We consider this extended version of the
theory in detail. We perform a perturbative analysis that includes all modes,
determine the propagators and discuss how including mixed-derivative terms
affects them. We also consider the Lifshitz scalar with mixed-derivative terms
as a toy model for power counting arguments and discuss the influence of such
terms on renormalizability.
|
[
{
"created": "Thu, 23 Oct 2014 13:26:09 GMT",
"version": "v1"
}
] |
2015-03-12
|
[
[
"Colombo",
"Mattia",
""
],
[
"Gumrukcuoglu",
"A. Emir",
""
],
[
"Sotiriou",
"Thomas P.",
""
]
] |
Horava gravity has been constructed so as to exhibit anisotropic scaling in the ultraviolet, as this renders the theory power-counting renormalizable. However, when coupled to matter, the theory has been shown to suffer from quadratic divergences. A way to cure these divergences is to add terms with both time and space derivatives. We consider this extended version of the theory in detail. We perform a perturbative analysis that includes all modes, determine the propagators and discuss how including mixed-derivative terms affects them. We also consider the Lifshitz scalar with mixed-derivative terms as a toy model for power counting arguments and discuss the influence of such terms on renormalizability.
|
hep-th/9802159
|
Zoltan Nemeth
|
Z. Nemeth
|
Remarks on the solutions of the Maxwell- Chern-Simons theories
|
9 pages, Plain Tex
|
Phys.Rev.D58:067703,1998
|
10.1103/PhysRevD.58.067703
| null |
hep-th
| null |
The large distance behavior of the Maxwell- Chern-Simons (MCS) equations is
analyzed, and it is found that the pure Chern-Simons limit, (when the Maxwell
term is dropped from the equations), does not describe the large distance limit
of the MCS model. This necessitates the solution of the original problem. The
MCS gauge theory coupled to a nonrelativistic matter field, (governed by the
gauged non-linear Schr\"odinger equation), is studied. It turns out, that there
are no regular self-dual solutions as in the pure Chern-Simons case, but the
model admits interesting, though singular self-dual solutions. The properties
of these solutions, and their large distance limits are analyzed.
|
[
{
"created": "Mon, 23 Feb 1998 13:20:21 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Nemeth",
"Z.",
""
]
] |
The large distance behavior of the Maxwell- Chern-Simons (MCS) equations is analyzed, and it is found that the pure Chern-Simons limit, (when the Maxwell term is dropped from the equations), does not describe the large distance limit of the MCS model. This necessitates the solution of the original problem. The MCS gauge theory coupled to a nonrelativistic matter field, (governed by the gauged non-linear Schr\"odinger equation), is studied. It turns out, that there are no regular self-dual solutions as in the pure Chern-Simons case, but the model admits interesting, though singular self-dual solutions. The properties of these solutions, and their large distance limits are analyzed.
|
hep-th/0409164
|
Haba Zbigniew
|
Z. Haba
|
Green functions and propagation of waves in strongly inhomogeneous media
| null |
J.Phys.A37:9295,2004
|
10.1088/0305-4470/37/39/015
| null |
hep-th
| null |
We show that Green functions of second-order differential operators with
singular or unbounded coefficients can have an anomalous behaviour in
comparison to the well-known properties of Green functions of operators with
bounded coefficients. We discuss some consequences of such an anomalous short
or long distance behaviour for a diffusion and wave propagation in an
inhomogeneous medium.
|
[
{
"created": "Wed, 15 Sep 2004 20:48:12 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Haba",
"Z.",
""
]
] |
We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded coefficients. We discuss some consequences of such an anomalous short or long distance behaviour for a diffusion and wave propagation in an inhomogeneous medium.
|
1005.4654
|
Christopher Pope
|
J.T. Liu and C.N. Pope
|
Inconsistency of Breathing Mode Extensions of Maximal Five-Dimensional
Supergravity Embedding
|
16 pages
| null |
10.1007/JHEP06(2012)067
|
MCTP-10-19, MIFPA-10-23
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Recent work on consistent Kaluza-Klein reductions on Einstein-Sasaki spaces
prompted an intriguing conjecture that there might exist a consistent $S^5$
reduction of type IIB supergravity to give five-dimensional ${\cal N}=8$ gauged
supergravity coupled to a massive supermultiplet that includes the
breathing-mode scalar. Motivated by this, we investigate the possibility of
augmenting the usual ${\cal N}=8$ supergravity reduction to include a
breathing-mode scalar, and we show that this is in fact inconsistent. The
standard reduction to the massless ${\cal N}=8$ supermultiplet depends for its
consistency on a delicate interplay between properties of the ten-dimensional
type IIB theory and properties of the Killing vectors on $S^5$. Our
calculations show that turning on the breathing-mode is sufficient to destroy
the balance, and hence render the reduction inconsistent.
|
[
{
"created": "Tue, 25 May 2010 18:43:15 GMT",
"version": "v1"
}
] |
2015-05-19
|
[
[
"Liu",
"J. T.",
""
],
[
"Pope",
"C. N.",
""
]
] |
Recent work on consistent Kaluza-Klein reductions on Einstein-Sasaki spaces prompted an intriguing conjecture that there might exist a consistent $S^5$ reduction of type IIB supergravity to give five-dimensional ${\cal N}=8$ gauged supergravity coupled to a massive supermultiplet that includes the breathing-mode scalar. Motivated by this, we investigate the possibility of augmenting the usual ${\cal N}=8$ supergravity reduction to include a breathing-mode scalar, and we show that this is in fact inconsistent. The standard reduction to the massless ${\cal N}=8$ supermultiplet depends for its consistency on a delicate interplay between properties of the ten-dimensional type IIB theory and properties of the Killing vectors on $S^5$. Our calculations show that turning on the breathing-mode is sufficient to destroy the balance, and hence render the reduction inconsistent.
|
0912.4664
|
Dongmin Gang
|
Dongmin Gang
|
Chern-Simons theory on L(p,q) lens spaces and Localization
|
25 pages, v2: In S2XS1 case, monopole comtributations added. Appendix
on monopole harmonics added. References added. Mistakes corrected
| null |
10.3938/jkps.74.1119
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Using localization technique, we calculate the partition function and the
expectation value of Wilson loop operator in Chern-Simons theory on general
lens spaces L(p,q)(including S2XS1). Our results are consistent with known
results.
|
[
{
"created": "Wed, 23 Dec 2009 20:15:21 GMT",
"version": "v1"
},
{
"created": "Mon, 1 Feb 2010 11:37:29 GMT",
"version": "v2"
}
] |
2019-12-04
|
[
[
"Gang",
"Dongmin",
""
]
] |
Using localization technique, we calculate the partition function and the expectation value of Wilson loop operator in Chern-Simons theory on general lens spaces L(p,q)(including S2XS1). Our results are consistent with known results.
|
1108.5179
|
James T. Liu
|
James T. Liu and Zhichen Zhao
|
A holographic c-theorem for higher derivative gravity
|
12 pages
| null | null |
MCTP-11-32
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We prove a holographic c-theorem for the a central charge in AdS/CFT where
the bulk is described by a gravitational action built out of an arbitrary
function f(R^{ab}_{cd}) of the Riemann tensor coupled to bulk matter. This
theorem holds provided a generalized null energy condition involving both
matter and higher curvature gravitational interactions is satisfied. As an
example, we consider the case of a curvature-squared action, and find that
generically the generalized null energy condition involves not just the bulk
matter, but also the sign of R" where a prime denotes a radial derivative and
where R is the bulk scalar curvature.
|
[
{
"created": "Thu, 25 Aug 2011 20:01:06 GMT",
"version": "v1"
}
] |
2011-08-29
|
[
[
"Liu",
"James T.",
""
],
[
"Zhao",
"Zhichen",
""
]
] |
We prove a holographic c-theorem for the a central charge in AdS/CFT where the bulk is described by a gravitational action built out of an arbitrary function f(R^{ab}_{cd}) of the Riemann tensor coupled to bulk matter. This theorem holds provided a generalized null energy condition involving both matter and higher curvature gravitational interactions is satisfied. As an example, we consider the case of a curvature-squared action, and find that generically the generalized null energy condition involves not just the bulk matter, but also the sign of R" where a prime denotes a radial derivative and where R is the bulk scalar curvature.
|
1607.06817
|
Martin Ammon
|
Martin Ammon, Sebastian Grieninger, Amadeo Jimenez-Alba, Rodrigo P.
Macedo, Luis Melgar
|
Holographic quenches and anomalous transport
|
34 pages, 10 figures
| null |
10.1007/JHEP09(2016)131
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study the response of the chiral magnetic effect due to continuous
quenches induced by time dependent electric fields within holography.
Concretely, we consider a holographic model with dual chiral anomaly and
compute the electric current parallel to a constant, homogeneous magnetic field
and a time dependent electric field in the probe approximation. We explicitly
solve the PDEs by means of pseudospectral methods in spatial and time
directions and study the transition to an universal "fast" quench response.
Moreover, we compute the amplitudes, i.e.,~residues of the quasi normal modes,
by solving the (ODE) Laplace transformed equations. We investigate the
possibility of considering the asymptotic growth rate of the amplitudes as a
well defined notion of initial time scale for linearized systems. Finally, we
highlight the existence of Landau level resonances in the electrical
conductivity parallel to a magnetic field at finite frequency and show
explicitly that these only appear in presence of the anomaly. We show that the
existence of these resonances induces, among others, a long-lived AC electric
current once the electric field is switched off.
|
[
{
"created": "Fri, 22 Jul 2016 20:00:06 GMT",
"version": "v1"
},
{
"created": "Fri, 22 Sep 2017 12:17:09 GMT",
"version": "v2"
}
] |
2017-09-25
|
[
[
"Ammon",
"Martin",
""
],
[
"Grieninger",
"Sebastian",
""
],
[
"Jimenez-Alba",
"Amadeo",
""
],
[
"Macedo",
"Rodrigo P.",
""
],
[
"Melgar",
"Luis",
""
]
] |
We study the response of the chiral magnetic effect due to continuous quenches induced by time dependent electric fields within holography. Concretely, we consider a holographic model with dual chiral anomaly and compute the electric current parallel to a constant, homogeneous magnetic field and a time dependent electric field in the probe approximation. We explicitly solve the PDEs by means of pseudospectral methods in spatial and time directions and study the transition to an universal "fast" quench response. Moreover, we compute the amplitudes, i.e.,~residues of the quasi normal modes, by solving the (ODE) Laplace transformed equations. We investigate the possibility of considering the asymptotic growth rate of the amplitudes as a well defined notion of initial time scale for linearized systems. Finally, we highlight the existence of Landau level resonances in the electrical conductivity parallel to a magnetic field at finite frequency and show explicitly that these only appear in presence of the anomaly. We show that the existence of these resonances induces, among others, a long-lived AC electric current once the electric field is switched off.
|
1608.06252
|
Bom Soo Kim
|
Bom Soo Kim
|
Holographic Renormalization of Einstein-Maxwell-Dilaton Theories
|
39+1 pages. Improved discussions, typos fixed and references added
|
JHEP 1611 (2016) 044
|
10.1007/JHEP11(2016)044
| null |
hep-th cond-mat.str-el
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We generalize the boundary value problem with a mixed boundary condition that
involves the gauge and scalar fields in the context of Einstein-Maxwell-Dilaton
theories. In particular, the expectation value of the dual scalar operator can
be a function of the expectation value of the current operator. The properties
are prevalent in a fixed charge ensemble because the conserved charge is shared
by both fields through the dilaton coupling, which is also responsible for
non-Fermi liquid properties. We study the on-shell action and the stress energy
tensor to note practical importances of the boundary value problem. In the
presence of the scalar fields, physical quantities are not fully fixed due to
the finite boundary terms that manifest in the massless scalar or the scalar
with mass saturating the Breitenlohner-Freedman bound.
|
[
{
"created": "Mon, 22 Aug 2016 18:19:58 GMT",
"version": "v1"
},
{
"created": "Thu, 8 Sep 2016 21:38:59 GMT",
"version": "v2"
}
] |
2017-03-23
|
[
[
"Kim",
"Bom Soo",
""
]
] |
We generalize the boundary value problem with a mixed boundary condition that involves the gauge and scalar fields in the context of Einstein-Maxwell-Dilaton theories. In particular, the expectation value of the dual scalar operator can be a function of the expectation value of the current operator. The properties are prevalent in a fixed charge ensemble because the conserved charge is shared by both fields through the dilaton coupling, which is also responsible for non-Fermi liquid properties. We study the on-shell action and the stress energy tensor to note practical importances of the boundary value problem. In the presence of the scalar fields, physical quantities are not fully fixed due to the finite boundary terms that manifest in the massless scalar or the scalar with mass saturating the Breitenlohner-Freedman bound.
|
0803.0303
|
Roberto Percacci
|
R. Percacci
|
Mixing internal and spacetime transformations: some examples and
counterexamples
|
Plain TEX, 6 pages
|
J.Phys.A41:335403,2008
|
10.1088/1751-8113/41/33/335403
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
This note addresses the question whether in a gauge theory coupled to gravity
internal and spacetime transformation can be mixed. It is shown that if the VEV
of the gauge field is flat, the symmetry group is always a product of internal
and spacetime symmetries. On the other hand, if the VEV of the gauge field is
not flat it is impossible to properly define the notion of a ``spacetime''
transformation; as a consequence, if the symmetry group is nontrivial, mixing
generically occurs.
|
[
{
"created": "Mon, 3 Mar 2008 19:06:11 GMT",
"version": "v1"
}
] |
2008-11-26
|
[
[
"Percacci",
"R.",
""
]
] |
This note addresses the question whether in a gauge theory coupled to gravity internal and spacetime transformation can be mixed. It is shown that if the VEV of the gauge field is flat, the symmetry group is always a product of internal and spacetime symmetries. On the other hand, if the VEV of the gauge field is not flat it is impossible to properly define the notion of a ``spacetime'' transformation; as a consequence, if the symmetry group is nontrivial, mixing generically occurs.
|
hep-th/0103133
|
Marco M. Caldarelli
|
M. M. Caldarelli, D. Klemm, W. A. Sabra
|
Causality Violation and Naked Time Machines in AdS_5
|
22 pages, Latex, uses JHEP.cls, 1 figure. v3: comments on unitarity
in CFT and 2 references added. v4: changes in final remarks, final version to
appear in JHEP
|
JHEP 0105 (2001) 014
|
10.1088/1126-6708/2001/05/014
| null |
hep-th gr-qc
| null |
We study supersymmetric charged rotating black holes in AdS$_5$, and show
that closed timelike curves occur outside the event horizon. Also upon lifting
to rotating D3 brane solutions of type IIB supergravity in ten dimensions,
closed timelike curves are still present. We believe that these causal
anomalies correspond to loss of unitarity in the dual ${\cal N}=4$, D=4 super
Yang-Mills theory, i.e. the chronology protection conjecture in the AdS bulk is
related to unitarity bounds in the boundary CFT. We show that no charged or
uncharged geodesic can penetrate the horizon, so that the exterior region is
geodesically complete. These results still hold true in the quantum case,
i.~e.~the total absorption cross section for Klein-Gordon scalars propagating
in the black hole background is zero. This suggests that the effective
temperature is zero instead of assuming the naively found imaginary value.
|
[
{
"created": "Fri, 16 Mar 2001 19:10:34 GMT",
"version": "v1"
},
{
"created": "Sun, 18 Mar 2001 19:48:45 GMT",
"version": "v2"
},
{
"created": "Sun, 8 Apr 2001 18:48:40 GMT",
"version": "v3"
},
{
"created": "Mon, 7 May 2001 17:13:29 GMT",
"version": "v4"
}
] |
2009-11-07
|
[
[
"Caldarelli",
"M. M.",
""
],
[
"Klemm",
"D.",
""
],
[
"Sabra",
"W. A.",
""
]
] |
We study supersymmetric charged rotating black holes in AdS$_5$, and show that closed timelike curves occur outside the event horizon. Also upon lifting to rotating D3 brane solutions of type IIB supergravity in ten dimensions, closed timelike curves are still present. We believe that these causal anomalies correspond to loss of unitarity in the dual ${\cal N}=4$, D=4 super Yang-Mills theory, i.e. the chronology protection conjecture in the AdS bulk is related to unitarity bounds in the boundary CFT. We show that no charged or uncharged geodesic can penetrate the horizon, so that the exterior region is geodesically complete. These results still hold true in the quantum case, i.~e.~the total absorption cross section for Klein-Gordon scalars propagating in the black hole background is zero. This suggests that the effective temperature is zero instead of assuming the naively found imaginary value.
|
hep-th/0206190
|
Takao Koikawa
|
Takayuki Hori, Takao Koikawa and Takuya Maki
|
Moyal Quantization for Constrained System
|
25 pages
|
Prog.Theor.Phys. 108 (2002) 1123-1141
|
10.1143/PTP.108.1123
| null |
hep-th
| null |
We study the Moyal quantization for the constrained system. One of the
purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence,
which connects the Weyl symbols with the corresponding quantum operators. A
Hamiltonian in terms of the Weyl symbols becomes different from the classical
Hamiltonian for the constrained system, which is related to the fact that the
naively constructed WW correspondence is not one-to-one any more. In the Moyal
quantization a geometrical meaning of the constraints is clear. In our
proposal, the 2nd class constraints are incorporated into the definition of the
WW correspondence by limiting the phasespace to the hypersurface. Even though
we assume the canonical commutation relations in the formulation, the Moyal
brackets between the Weyl symbols yield the same results as those for the
constrained system derived by using the Dirac bracket formulation.
|
[
{
"created": "Thu, 20 Jun 2002 13:41:21 GMT",
"version": "v1"
}
] |
2009-11-07
|
[
[
"Hori",
"Takayuki",
""
],
[
"Koikawa",
"Takao",
""
],
[
"Maki",
"Takuya",
""
]
] |
We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in terms of the Weyl symbols becomes different from the classical Hamiltonian for the constrained system, which is related to the fact that the naively constructed WW correspondence is not one-to-one any more. In the Moyal quantization a geometrical meaning of the constraints is clear. In our proposal, the 2nd class constraints are incorporated into the definition of the WW correspondence by limiting the phasespace to the hypersurface. Even though we assume the canonical commutation relations in the formulation, the Moyal brackets between the Weyl symbols yield the same results as those for the constrained system derived by using the Dirac bracket formulation.
|
2407.08581
|
Yiwen Huang
|
Timothy Cohen, Daniel Green, and Yiwen Huang
|
Operator Origin of Anomalous Dimensions in de Sitter Space
|
42 pages, 5 figures
| null | null | null |
hep-th astro-ph.CO hep-ph
|
http://creativecommons.org/licenses/by/4.0/
|
The late time limit of the power spectrum for heavy (principal series) fields
in de Sitter space yields a series of polynomial terms with complex scaling
dimensions. Such scaling behavior is expected to result from an associated
operator with a complex dimension. In a free theory, these complex dimensions
are known to match the constraints imposed by unitarity on the space of states.
Yet, perturbative corrections to the scaling behavior of operators are naively
inconsistent with unitary evolution of the quantum fields in dS. This paper
demonstrates how to compute one-loop corrections to the scaling dimensions that
appear in the two point function from the field theory description in terms of
local operators. We first show how to evaluate these anomalous dimensions using
Mellin space, which has the feature that it naturally accommodates a scaleless
regulator. We then explore the consequences for the Soft de Sitter Effective
Theory (SdSET) description that emerges in the long wavelength limit. Carefully
matching between the UV and SdSET descriptions requires the introduction of
novel non-dynamical "operators" in the effective theory. This is not only
necessary to reproduce results extracted from the K\"all\'en-Lehmann
representation (that use the space of unitary states directly), but it is also
required by general arguments that invoke positivity.
|
[
{
"created": "Thu, 11 Jul 2024 15:07:02 GMT",
"version": "v1"
}
] |
2024-07-12
|
[
[
"Cohen",
"Timothy",
""
],
[
"Green",
"Daniel",
""
],
[
"Huang",
"Yiwen",
""
]
] |
The late time limit of the power spectrum for heavy (principal series) fields in de Sitter space yields a series of polynomial terms with complex scaling dimensions. Such scaling behavior is expected to result from an associated operator with a complex dimension. In a free theory, these complex dimensions are known to match the constraints imposed by unitarity on the space of states. Yet, perturbative corrections to the scaling behavior of operators are naively inconsistent with unitary evolution of the quantum fields in dS. This paper demonstrates how to compute one-loop corrections to the scaling dimensions that appear in the two point function from the field theory description in terms of local operators. We first show how to evaluate these anomalous dimensions using Mellin space, which has the feature that it naturally accommodates a scaleless regulator. We then explore the consequences for the Soft de Sitter Effective Theory (SdSET) description that emerges in the long wavelength limit. Carefully matching between the UV and SdSET descriptions requires the introduction of novel non-dynamical "operators" in the effective theory. This is not only necessary to reproduce results extracted from the K\"all\'en-Lehmann representation (that use the space of unitary states directly), but it is also required by general arguments that invoke positivity.
|
1010.3634
|
Jean Alexandre
|
Jean Alexandre, Pavlos Pasipoularides
|
Spherically symmetric solutions in Covariant Horava-Lifshitz Gravity
|
29 pages, comments and figure added
|
Phys.Rev.D83:084030,2011
|
10.1103/PhysRevD.83.084030
| null |
hep-th gr-qc hep-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study the most general case of spherically symmetric vacuum solutions in
the framework of the Covariant Horava Lifshitz Gravity, for an action that
includes all possible higher order terms in curvature which are compatible with
power-counting normalizability requirement. We find that solutions can be
separated into two main classes: (i) solutions with nonzero radial shift
function, and (ii) solutions with zero radial shift function. In the case (ii),
spherically symmetric solutions are consistent with observations if we adopt
the view of Horava and Melby-Tomson, according to which the auxiliary field A
can be considered as a part of an effective general relativistic metric, which
is valid only in the IR limit. On the other hand, in the case (i), consistency
with observations implies that the field A should be independent of the
spacetime geometry, as the Newtonian potential arises from the nonzero radial
shift function. Also, our aim in this paper is to discuss and compare these two
alternative but different assumptions for the auxiliary field A.
|
[
{
"created": "Mon, 18 Oct 2010 15:42:36 GMT",
"version": "v1"
},
{
"created": "Mon, 25 Oct 2010 12:53:06 GMT",
"version": "v2"
},
{
"created": "Fri, 25 Mar 2011 21:46:41 GMT",
"version": "v3"
}
] |
2011-04-29
|
[
[
"Alexandre",
"Jean",
""
],
[
"Pasipoularides",
"Pavlos",
""
]
] |
We study the most general case of spherically symmetric vacuum solutions in the framework of the Covariant Horava Lifshitz Gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability requirement. We find that solutions can be separated into two main classes: (i) solutions with nonzero radial shift function, and (ii) solutions with zero radial shift function. In the case (ii), spherically symmetric solutions are consistent with observations if we adopt the view of Horava and Melby-Tomson, according to which the auxiliary field A can be considered as a part of an effective general relativistic metric, which is valid only in the IR limit. On the other hand, in the case (i), consistency with observations implies that the field A should be independent of the spacetime geometry, as the Newtonian potential arises from the nonzero radial shift function. Also, our aim in this paper is to discuss and compare these two alternative but different assumptions for the auxiliary field A.
|
1712.01710
|
Yu-xin Liu
|
Chong-yao Chen, Fei Gao, and Yu-xin Liu
|
A modification of Faddeev-Popov approach free from Gribov ambiguity
|
8 pages, no figure, typos corrected
|
Commun. Theor. Phys. 72, 125201 (2020)
|
10.1088/1572-9494/abb7cb
| null |
hep-th hep-ph nucl-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We propose a modified version of the Faddeev-Popov quantization approach for
non-Abelian gauge field theory to avoid the Gribov ambiguity. We show that by
means of introducing a new method to insert the correct identity into the
Yang-Mills generating functional and considering the identity generated by an
integral through a subgroup of the gauge group, the problem of the Gribov
ambiguity can be removed naturally. Meanwhile by handling the absolute value of
the Faddeev-Popov determinant with the method introduced by Williams and
collaborators, we lift the Jacobian determinant together with the absolute
value and obtain a local Lagrangian. The new Lagrangian have a nilpotent
symmetry which can be viewed as an analogue of the BRST symmetry.
|
[
{
"created": "Tue, 5 Dec 2017 15:21:46 GMT",
"version": "v1"
},
{
"created": "Wed, 13 Dec 2017 02:52:02 GMT",
"version": "v2"
},
{
"created": "Fri, 8 Jun 2018 15:11:57 GMT",
"version": "v3"
}
] |
2021-09-22
|
[
[
"Chen",
"Chong-yao",
""
],
[
"Gao",
"Fei",
""
],
[
"Liu",
"Yu-xin",
""
]
] |
We propose a modified version of the Faddeev-Popov quantization approach for non-Abelian gauge field theory to avoid the Gribov ambiguity. We show that by means of introducing a new method to insert the correct identity into the Yang-Mills generating functional and considering the identity generated by an integral through a subgroup of the gauge group, the problem of the Gribov ambiguity can be removed naturally. Meanwhile by handling the absolute value of the Faddeev-Popov determinant with the method introduced by Williams and collaborators, we lift the Jacobian determinant together with the absolute value and obtain a local Lagrangian. The new Lagrangian have a nilpotent symmetry which can be viewed as an analogue of the BRST symmetry.
|
1011.2172
|
Jorge Russo
|
Francesco Aprile, Diego Rodriguez-Gomez and Jorge G. Russo
|
p-wave Holographic Superconductors and five-dimensional gauged
Supergravity
|
35 pages, 14 figures
|
JHEP 1101:056,2011
|
10.1007/JHEP01(2011)056
|
ICCUB-10-104
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We explore five-dimensional ${\cal N}=4$ $SU(2)\times U(1)$ and ${\cal N}=8$
SO(6) gauged supergravities as frameworks for condensed matter applications.
These theories contain charged (dilatonic) black holes and 2-forms which have
non-trivial quantum numbers with respect to U(1) subgroups of SO(6). A question
of interest is whether they also contain black holes with two-form hair with
the required asymptotic to give rise to holographic superconductivity. We first
consider the ${\cal N}=4$ case, which contains a complex two-form potential
$A_{\mu\nu}$ which has U(1) charge $\pm 1$. We find that a slight
generalization, where the two-form potential has an arbitrary charge $q$, leads
to a five-dimensional model that exhibits second-order superconducting
transitions of p-wave type where the role of order parameter is played by
$A_{\mu\nu}$, provided $q \gtrsim 5.6$. We identify the operator that condenses
in the dual CFT, which is closely related to ${\cal N}=4$ Super Yang-Mills
theory with chemical potentials. Similar phase transitions between R-charged
black holes and black holes with 2-form hair are found in a generalized version
of the ${\cal N}=8$ gauged supergravity Lagrangian where the two-forms have
charge $q\gtrsim 1.8$.
|
[
{
"created": "Tue, 9 Nov 2010 18:55:10 GMT",
"version": "v1"
},
{
"created": "Wed, 17 Nov 2010 18:11:22 GMT",
"version": "v2"
},
{
"created": "Wed, 15 Dec 2010 13:28:54 GMT",
"version": "v3"
}
] |
2011-06-21
|
[
[
"Aprile",
"Francesco",
""
],
[
"Rodriguez-Gomez",
"Diego",
""
],
[
"Russo",
"Jorge G.",
""
]
] |
We explore five-dimensional ${\cal N}=4$ $SU(2)\times U(1)$ and ${\cal N}=8$ SO(6) gauged supergravities as frameworks for condensed matter applications. These theories contain charged (dilatonic) black holes and 2-forms which have non-trivial quantum numbers with respect to U(1) subgroups of SO(6). A question of interest is whether they also contain black holes with two-form hair with the required asymptotic to give rise to holographic superconductivity. We first consider the ${\cal N}=4$ case, which contains a complex two-form potential $A_{\mu\nu}$ which has U(1) charge $\pm 1$. We find that a slight generalization, where the two-form potential has an arbitrary charge $q$, leads to a five-dimensional model that exhibits second-order superconducting transitions of p-wave type where the role of order parameter is played by $A_{\mu\nu}$, provided $q \gtrsim 5.6$. We identify the operator that condenses in the dual CFT, which is closely related to ${\cal N}=4$ Super Yang-Mills theory with chemical potentials. Similar phase transitions between R-charged black holes and black holes with 2-form hair are found in a generalized version of the ${\cal N}=8$ gauged supergravity Lagrangian where the two-forms have charge $q\gtrsim 1.8$.
|
0705.1338
|
Francisco A. Brito
|
F.A. Brito, J.R. Nascimento, E. Passos, and A. Petrov
|
Lorentz-CPT violation, radiative corrections and finite temperature
|
To appear in JHEP, 10 pages, 1 eps figure, minor changes and
references added
|
JHEP 0706:016,2007
|
10.1088/1126-6708/2007/06/016
| null |
hep-th
| null |
In this work we investigate the radiatively induced Chern-Simons-like terms
in four-dimensions at zero and finite temperature. We use the approach of
rationalizing the fermion propagator up to the leading order in the
CPT-violating coupling $b_\mu$. In this approach, we have shown that although
the coefficient of Chern-Simons term can be found unambiguously in different
regularization schemes at zero or finite temperature, it remains undetermined.
We observe a correspondence among results obtained at finite and zero
temperature.
|
[
{
"created": "Wed, 9 May 2007 18:00:26 GMT",
"version": "v1"
},
{
"created": "Fri, 1 Jun 2007 18:50:42 GMT",
"version": "v2"
}
] |
2009-11-13
|
[
[
"Brito",
"F. A.",
""
],
[
"Nascimento",
"J. R.",
""
],
[
"Passos",
"E.",
""
],
[
"Petrov",
"A.",
""
]
] |
In this work we investigate the radiatively induced Chern-Simons-like terms in four-dimensions at zero and finite temperature. We use the approach of rationalizing the fermion propagator up to the leading order in the CPT-violating coupling $b_\mu$. In this approach, we have shown that although the coefficient of Chern-Simons term can be found unambiguously in different regularization schemes at zero or finite temperature, it remains undetermined. We observe a correspondence among results obtained at finite and zero temperature.
|
hep-th/9410025
|
Vasily Tarasov
|
Vasily E. Tarasov
|
Dissipative Quantum Mechanics: The Generalization of the Canonical
Quantization and von Neumann Equation
|
23 pages, LaTex
| null | null |
IC-94-192
|
hep-th cond-mat
| null |
The dissipative models in string theory can have more broad range of
application: 1) Noncritical strings are dissipative systems in the "coupling
constant" phase space. 2) Bosonic string in the affine-metric curved space is
dissipative system.
But the quantum descriptions of the dissipative systems have well known
ambiguities. In order to solve the problems of the quantum description of
dissipative systems we suggest to introduce an operator W in addition to usual
(associative) operators. The suggested operator algebra does not violate
Heisenberg algebra because we extend the canonical commutation relations by
introducing an operator W of the nonholonomic quantities in addition to the
usual (associative) operators of usual (holonomic) coordinate -momentum
functions. To satisfy the generalized commutation relations the operator W must
be nonassociative nonLieble (does not satisfied the Jacobi identity) operator.
As the result of these properties the total time derivative of the
multiplication and commutator of the operators does not satisfies the Leibnitz
rule. This lead to compatibility of quantum equations of motion for dissipative
systems and canonical commutation relations. The suggested generalization of
the von Neumann equation is connected with classical Liouville equation for
dissipative systems.
|
[
{
"created": "Wed, 5 Oct 1994 19:29:00 GMT",
"version": "v1"
},
{
"created": "Wed, 7 Jun 1995 16:17:30 GMT",
"version": "v2"
}
] |
2008-02-03
|
[
[
"Tarasov",
"Vasily E.",
""
]
] |
The dissipative models in string theory can have more broad range of application: 1) Noncritical strings are dissipative systems in the "coupling constant" phase space. 2) Bosonic string in the affine-metric curved space is dissipative system. But the quantum descriptions of the dissipative systems have well known ambiguities. In order to solve the problems of the quantum description of dissipative systems we suggest to introduce an operator W in addition to usual (associative) operators. The suggested operator algebra does not violate Heisenberg algebra because we extend the canonical commutation relations by introducing an operator W of the nonholonomic quantities in addition to the usual (associative) operators of usual (holonomic) coordinate -momentum functions. To satisfy the generalized commutation relations the operator W must be nonassociative nonLieble (does not satisfied the Jacobi identity) operator. As the result of these properties the total time derivative of the multiplication and commutator of the operators does not satisfies the Leibnitz rule. This lead to compatibility of quantum equations of motion for dissipative systems and canonical commutation relations. The suggested generalization of the von Neumann equation is connected with classical Liouville equation for dissipative systems.
|
hep-th/9509089
|
Lorenzo Luis Salcedo Moreno
|
L.L. Salcedo
|
Absence of classical and quantum mixing
|
REVTeX, 4 pages
|
Phys.Rev. A54 (1996) 3657-3660
|
10.1103/PhysRevA.54.3657
|
UG-DFM-11/95
|
hep-th quant-ph
| null |
It is shown, under mild assumptions, that classical degrees of freedom
dynamically coupled to quantum ones do not inherit their quantum fluctuations.
It is further shown that, if the assumptions are strengthen by imposing the
existence of a canonical structure, only purely classical or purely quantum
dynamics are allowed.
|
[
{
"created": "Fri, 15 Sep 1995 12:49:38 GMT",
"version": "v1"
}
] |
2009-10-28
|
[
[
"Salcedo",
"L. L.",
""
]
] |
It is shown, under mild assumptions, that classical degrees of freedom dynamically coupled to quantum ones do not inherit their quantum fluctuations. It is further shown that, if the assumptions are strengthen by imposing the existence of a canonical structure, only purely classical or purely quantum dynamics are allowed.
|
hep-th/0703161
|
Om Prakash Singh Negi
|
Seema Rawat and O. P. S. Negi
|
Quaternionic Formulation of Supersymmetric Quantum Mechanics
| null |
Int.J.Theor.Phys.48:305-314,2009
|
10.1007/s10773-008-9803-1
| null |
hep-th
| null |
Quaternionic formulation of supersymmetric quantum mechanics has been
developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and
supercharges for free particle and interacting field in one and three
dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are
discussed and it has been shown that the results are consistent with the
results of quantum mechanics.
|
[
{
"created": "Sun, 18 Mar 2007 17:35:21 GMT",
"version": "v1"
}
] |
2009-02-18
|
[
[
"Rawat",
"Seema",
""
],
[
"Negi",
"O. P. S.",
""
]
] |
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
|
hep-th/9502021
|
Andrea Cappelli
|
Andrea Cappelli, Carlo A. Trugenberger and Guillermo R. Zemba
|
Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal
Models
|
Latex file, 41 pages
|
Nucl.Phys. B448 (1995) 470
|
10.1016/0550-3213(95)00233-I
|
preprint UGVA-DPT 1995/01-870 and DFTT 09/95
|
hep-th cond-mat
| null |
In this paper, we pursue our analysis of the W-infinity symmetry of the
low-energy edge excitations of incompressible quantum Hall fluids. These
excitations are described by (1+1)-dimensional effective field theories, which
are built by representations of the W-infinity algebra. Generic W-infinity
theories predict many more fluids than the few, stable ones found in
experiments. Here we identify a particular class of W-infinity theories, the
minimal models, which are made of degenerate representations only - a familiar
construction in conformal field theory. The W-infinity minimal models exist for
specific values of the fractional conductivity, which nicely fit the
experimental data and match the results of the Jain hierarchy of quantum Hall
fluids. We thus obtain a new hierarchical construction, which is based uniquely
on the concept of quantum incompressible fluid and is independent of Jain's
approach and hypotheses. Furthermore, a surprising non-Abelian structure is
found in the W-infinity minimal models: they possess neutral quark-like
excitations with SU(m) quantum numbers and non-Abelian fractional statistics.
The physical electron is made of anyon and quark excitations. We discuss some
properties of these neutral excitations which could be seen in experiments and
numerical simulations.
|
[
{
"created": "Fri, 3 Feb 1995 19:55:11 GMT",
"version": "v1"
}
] |
2016-09-06
|
[
[
"Cappelli",
"Andrea",
""
],
[
"Trugenberger",
"Carlo A.",
""
],
[
"Zemba",
"Guillermo R.",
""
]
] |
In this paper, we pursue our analysis of the W-infinity symmetry of the low-energy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1+1)-dimensional effective field theories, which are built by representations of the W-infinity algebra. Generic W-infinity theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W-infinity theories, the minimal models, which are made of degenerate representations only - a familiar construction in conformal field theory. The W-infinity minimal models exist for specific values of the fractional conductivity, which nicely fit the experimental data and match the results of the Jain hierarchy of quantum Hall fluids. We thus obtain a new hierarchical construction, which is based uniquely on the concept of quantum incompressible fluid and is independent of Jain's approach and hypotheses. Furthermore, a surprising non-Abelian structure is found in the W-infinity minimal models: they possess neutral quark-like excitations with SU(m) quantum numbers and non-Abelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral excitations which could be seen in experiments and numerical simulations.
|
1502.01711
|
Paolo Valtancoli
|
P. Valtancoli
|
Path integral and noncommutative poisson brackets
|
7 pages, no figures
| null | null | null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We find that in presence of noncommutative poisson brackets the relation
between Lagrangian and Hamiltonian is modified. We discuss this property by
using the path integral formalism for non-relativistic systems. We apply this
procedure to the harmonic oscillator with a minimal length.
|
[
{
"created": "Thu, 5 Feb 2015 20:48:55 GMT",
"version": "v1"
}
] |
2015-02-06
|
[
[
"Valtancoli",
"P.",
""
]
] |
We find that in presence of noncommutative poisson brackets the relation between Lagrangian and Hamiltonian is modified. We discuss this property by using the path integral formalism for non-relativistic systems. We apply this procedure to the harmonic oscillator with a minimal length.
|
hep-th/0110176
|
Horacio E. Camblong
|
Horacio E. Camblong, Carlos R. Ordonez
|
Renormalized Path Integral for the Two-Dimensional Delta-Function
Interaction
|
26 pages. The paper was significantly expanded and numerous equations
were added for the sake of clarity; the main results and conclusions are
unchanged
|
Phys.Rev. A65 (2002) 052123
|
10.1103/PhysRevA.65.052123
| null |
hep-th hep-ph math-ph math.MP nucl-th quant-ph
| null |
A path-integral approach for delta-function potentials is presented.
Particular attention is paid to the two-dimensional case, which illustrates the
realization of a quantum anomaly for a scale invariant problem in quantum
mechanics. Our treatment is based on an infinite summation of perturbation
theory that captures the nonperturbative nature of the delta-function bound
state. The well-known singular character of the two-dimensional delta-function
potential is dealt with by considering the renormalized path integral resulting
from a variety of schemes: dimensional, momentum-cutoff, and real-space
regularization. Moreover, compatibility of the bound-state and scattering
sectors is shown.
|
[
{
"created": "Fri, 19 Oct 2001 19:05:51 GMT",
"version": "v1"
},
{
"created": "Tue, 23 Oct 2001 19:55:08 GMT",
"version": "v2"
},
{
"created": "Wed, 30 Jan 2002 03:54:05 GMT",
"version": "v3"
},
{
"created": "Sun, 19 May 2002 12:40:42 GMT",
"version": "v4"
}
] |
2007-05-23
|
[
[
"Camblong",
"Horacio E.",
""
],
[
"Ordonez",
"Carlos R.",
""
]
] |
A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.
|
1103.4530
|
Martin Cederwall
|
Martin Cederwall, Ulf Gran and Bengt E.W. Nilsson
|
D=3, N=8 conformal supergravity and the Dragon window
|
plain tex, 24 pp v2: minor changes
|
JHEP 1109:101,2011
|
10.1007/JHEP09(2011)101
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We give a superspace description of D=3, N=8 supergravity. The formulation is
off-shell in the sense that the equations of motion are not implied by the
superspace constraints (but an action principle is not given). The multiplet
structure is unconventional, which we connect to the existence of a "Dragon
window", that is modules occurring in the supercurvature but not in the
supertorsion. According to Dragon's theorem this cannot happen above three
dimensions. We clarify the relevance of this window for going on the conformal
shell, and discuss some aspects of coupling to conformal matter.
|
[
{
"created": "Wed, 23 Mar 2011 14:25:00 GMT",
"version": "v1"
},
{
"created": "Thu, 16 Jun 2011 11:13:14 GMT",
"version": "v2"
},
{
"created": "Tue, 23 Aug 2011 08:41:34 GMT",
"version": "v3"
}
] |
2011-09-28
|
[
[
"Cederwall",
"Martin",
""
],
[
"Gran",
"Ulf",
""
],
[
"Nilsson",
"Bengt E. W.",
""
]
] |
We give a superspace description of D=3, N=8 supergravity. The formulation is off-shell in the sense that the equations of motion are not implied by the superspace constraints (but an action principle is not given). The multiplet structure is unconventional, which we connect to the existence of a "Dragon window", that is modules occurring in the supercurvature but not in the supertorsion. According to Dragon's theorem this cannot happen above three dimensions. We clarify the relevance of this window for going on the conformal shell, and discuss some aspects of coupling to conformal matter.
|
hep-th/9703196
|
Hugh Osborn
|
J.I. Latorre, H. Osborn
|
Modified Weak Energy Condition for the Energy Momentum Tensor in Quantum
Field Theory
|
27 pages, 1 figure, uses harvmac, epsf and boldmath (included).
Change of title and some text changes, form to be published
|
Nucl.Phys. B511 (1998) 737-759
|
10.1016/S0550-3213(97)00667-6
|
DAMTP 97/1
|
hep-th gr-qc
| null |
The weak energy condition is known to fail in general when applied to
expectation values of the the energy momentum tensor in flat space quantum
field theory. It is shown how the usual counter arguments against its validity
are no longer applicable if the states $|\psi \r$ for which the expectation
value is considered are restricted to a suitably defined subspace. A possible
natural restriction on $|\psi \r$ is suggested and illustrated by two quantum
mechanical examples based on a simple perturbed harmonic oscillator
Hamiltonian. The proposed alternative quantum weak energy condition is applied
to states formed by the action of scalar, vector and the energy momentum tensor
operators on the vacuum. We assume conformal invariance in order to determine
almost uniquely three-point functions involving the energy momentum tensor in
terms of a few parameters. The positivity conditions lead to non trivial
inequalities for these parameters. They are satisfied in free field theories,
except in one case for dimensions close to two. Further restrictions on $|\psi
\r$ are suggested which remove this problem. The inequalities which follow from
considering the state formed by applying the energy momentum tensor to the
vacuum are shown to imply that the coefficient of the topological term in the
expectation value of the trace of the energy momentum tensor in an arbitrary
curved space background is positive, in accord with calculations in free field
theories.
|
[
{
"created": "Thu, 27 Mar 1997 10:01:10 GMT",
"version": "v1"
},
{
"created": "Wed, 8 Oct 1997 09:29:12 GMT",
"version": "v2"
}
] |
2009-10-30
|
[
[
"Latorre",
"J. I.",
""
],
[
"Osborn",
"H.",
""
]
] |
The weak energy condition is known to fail in general when applied to expectation values of the the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states $|\psi \r$ for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on $|\psi \r$ is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on $|\psi \r$ are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories.
|
hep-th/9807092
|
Kirill Krasnov
|
Laurent Freidel and Kirill Krasnov (Penn State)
|
Spin Foam Models and the Classical Action Principle
|
65 pages, many figures (published version)
|
Adv.Theor.Math.Phys.2:1183-1247,1999
| null |
CGPG-98/4-5
|
hep-th gr-qc
| null |
We propose a new systematic approach that allows one to derive the spin foam
(state sum) model of a theory starting from the corresponding classical action
functional. It can be applied to any theory whose action can be written as that
of the BF theory plus a functional of the B field. Examples of such theories
include BF theories with or without cosmological term, Yang-Mills theories and
gravity in various spacetime dimensions. Our main idea is two-fold. First, we
propose to take into account in the path integral certain distributional
configurations of the B field in which it is concentrated along lower
dimensional hypersurfaces in spacetime. Second, using the notion of generating
functional we develop perturbation expansion techniques, with the role of the
free theory played by the BF theory. We test our approach on various theories
for which the corresponding spin foam (state sum) models are known. We find
that it exactly reproduces the known models for BF and 2D Yang-Mills theories.
For the BF theory with cosmological term in 3 and 4 dimensions we calculate the
terms of the transition amplitude that are of the first order in the
cosmological constant, and find an agreement with the corresponding first order
terms of the known state sum models. We discuss implications of our results for
existing quantum gravity models.
|
[
{
"created": "Mon, 13 Jul 1998 21:54:01 GMT",
"version": "v1"
},
{
"created": "Fri, 14 May 1999 14:24:56 GMT",
"version": "v2"
}
] |
2008-11-26
|
[
[
"Freidel",
"Laurent",
"",
"Penn State"
],
[
"Krasnov",
"Kirill",
"",
"Penn State"
]
] |
We propose a new systematic approach that allows one to derive the spin foam (state sum) model of a theory starting from the corresponding classical action functional. It can be applied to any theory whose action can be written as that of the BF theory plus a functional of the B field. Examples of such theories include BF theories with or without cosmological term, Yang-Mills theories and gravity in various spacetime dimensions. Our main idea is two-fold. First, we propose to take into account in the path integral certain distributional configurations of the B field in which it is concentrated along lower dimensional hypersurfaces in spacetime. Second, using the notion of generating functional we develop perturbation expansion techniques, with the role of the free theory played by the BF theory. We test our approach on various theories for which the corresponding spin foam (state sum) models are known. We find that it exactly reproduces the known models for BF and 2D Yang-Mills theories. For the BF theory with cosmological term in 3 and 4 dimensions we calculate the terms of the transition amplitude that are of the first order in the cosmological constant, and find an agreement with the corresponding first order terms of the known state sum models. We discuss implications of our results for existing quantum gravity models.
|
1111.6968
|
Li-Sheng Tseng
|
Li-Sheng Tseng, Shing-Tung Yau
|
Generalized Cohomologies and Supersymmetry
|
16 pages
| null | null | null |
hep-th math.DG math.SG
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We show that the complex cohomologies of Bott, Chern, and Aeppli and the
symplectic cohomologies of Tseng and Yau arise in the context of type II string
theory. Specifically, they can be used to count a subset of scalar moduli
fields in Minkowski compactification with RR fluxes in the presence of either
O5/D5 or O6/D6 brane sources, respectively. Further, we introduce a new set of
cohomologies within the generalized complex geometry framework which
interpolate between these known complex and symplectic cohomologies. The
generalized complex cohomologies play the analogous role for counting massless
fields for a general supersymmetric Minkowski type II compactification with
Ramond-Ramond flux.
|
[
{
"created": "Tue, 29 Nov 2011 20:44:41 GMT",
"version": "v1"
}
] |
2011-11-30
|
[
[
"Tseng",
"Li-Sheng",
""
],
[
"Yau",
"Shing-Tung",
""
]
] |
We show that the complex cohomologies of Bott, Chern, and Aeppli and the symplectic cohomologies of Tseng and Yau arise in the context of type II string theory. Specifically, they can be used to count a subset of scalar moduli fields in Minkowski compactification with RR fluxes in the presence of either O5/D5 or O6/D6 brane sources, respectively. Further, we introduce a new set of cohomologies within the generalized complex geometry framework which interpolate between these known complex and symplectic cohomologies. The generalized complex cohomologies play the analogous role for counting massless fields for a general supersymmetric Minkowski type II compactification with Ramond-Ramond flux.
|
hep-th/0106156
|
Gunter Scharf
|
Florin Constantinescu, Gunter Scharf
|
Quantum field components of supersymmetric multiplets
|
21 pages, no figures, latex 2e
| null | null | null |
hep-th
| null |
We adress the problem of Fock space representations of (free) multiplet
component fiels encountered in supersymmetric quantum field theory insisting on
positivity and causality. We look in detail on the scalar and Majorana
components of the chiral supersymmetric multiplet. Several Fock space
representations are introduced. The last section contains a short application
to the supersymmetric Epstein-Glaser method. The present paper is written in
the vane of axiomatic quantum field theory with applications to the causal
approach to supersymmetry.
|
[
{
"created": "Mon, 18 Jun 2001 12:43:22 GMT",
"version": "v1"
}
] |
2007-05-23
|
[
[
"Constantinescu",
"Florin",
""
],
[
"Scharf",
"Gunter",
""
]
] |
We adress the problem of Fock space representations of (free) multiplet component fiels encountered in supersymmetric quantum field theory insisting on positivity and causality. We look in detail on the scalar and Majorana components of the chiral supersymmetric multiplet. Several Fock space representations are introduced. The last section contains a short application to the supersymmetric Epstein-Glaser method. The present paper is written in the vane of axiomatic quantum field theory with applications to the causal approach to supersymmetry.
|
1811.05226
|
Manuel Calixto
|
M. Calixto
|
Massive conformal particles with non-Abelian charges from free
U(2N,2N)-twistor dynamics: quantization and coherent states
|
24 pages, no figures. The connection with Penrose incidence relations
and their generalization to the colored N>1 case has been further explained
|
Journal of Geometry and Physics 146 (2019) 103505
|
10.1016/j.geomphys.2019.103505
| null |
hep-th math-ph math.MP quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The inclusion of non-Abelian U(N) internal charges (other than the electric
charge) into Twistor Theory is accomplished through the concept of "colored
twistors" (ctwistors for short) transforming under the colored conformal
symmetry U(2N,2N). In particular, we are interested in 2N-ctwistors describing
colored spinless conformal massive particles with phase space
U(2N,2N)/[U(2N)xU(2N)]. Penrose formulas for incidence relations are
generalized to N>1. We propose U(2N)-gauge invariant Lagrangians for
2N-ctwistors and we quantize them through a bosonic representation,
interpreting quantum states as particle-hole excitations above the ground
state. The connection between the corresponding Hilbert (Fock-like with
constraints) space and the carrier space of a discrete series representation of
U(2N,2N) is established through a coherent space (holomorphic) representation.
|
[
{
"created": "Tue, 13 Nov 2018 11:37:21 GMT",
"version": "v1"
},
{
"created": "Tue, 9 Apr 2019 15:00:09 GMT",
"version": "v2"
}
] |
2022-02-25
|
[
[
"Calixto",
"M.",
""
]
] |
The inclusion of non-Abelian U(N) internal charges (other than the electric charge) into Twistor Theory is accomplished through the concept of "colored twistors" (ctwistors for short) transforming under the colored conformal symmetry U(2N,2N). In particular, we are interested in 2N-ctwistors describing colored spinless conformal massive particles with phase space U(2N,2N)/[U(2N)xU(2N)]. Penrose formulas for incidence relations are generalized to N>1. We propose U(2N)-gauge invariant Lagrangians for 2N-ctwistors and we quantize them through a bosonic representation, interpreting quantum states as particle-hole excitations above the ground state. The connection between the corresponding Hilbert (Fock-like with constraints) space and the carrier space of a discrete series representation of U(2N,2N) is established through a coherent space (holomorphic) representation.
|
1909.08530
|
Pablo Antonio Cano Molina-Ni\~nirola
|
Pablo A. Cano, Tomas Ortin, Pedro F. Ramirez
|
On the extremality bound of stringy black holes
|
22 pages
| null |
10.1007/JHEP02(2020)175
|
IFT-UAM/CSIC-19-125, IFUM-1079-FT
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
A mild version of the weak gravity conjecture (WGC) states that extremal
black holes have charge-to-mass ratio larger or equal than one when
higher-curvature interactions are taken into account. Since these corrections
become more relevant in the low-mass regime, this would allow the decay of
extremal black holes in terms of energy and charge conservation. Evidence in
this direction has been mainly given in the context of corrections to
Einstein-Maxwell theory. Here we compute corrections to the charge-to-mass
ratio of some dyonic extremal black holes explicitly embedded in the heterotic
string effective theory. We find that modifications of the extremality bound
depend on the solution considered, with the charge-to-mass ratio remaining
unchanged or deviating positively from one. Additionally, we observe that the
introduction of the higher-curvature terms increases the Wald entropy in all
cases considered, whose variation does not seem to be correlated with the
charge-to-mass ratio, contrary to the situation in Einstein-Maxwell theory.
|
[
{
"created": "Wed, 18 Sep 2019 16:04:05 GMT",
"version": "v1"
}
] |
2020-03-18
|
[
[
"Cano",
"Pablo A.",
""
],
[
"Ortin",
"Tomas",
""
],
[
"Ramirez",
"Pedro F.",
""
]
] |
A mild version of the weak gravity conjecture (WGC) states that extremal black holes have charge-to-mass ratio larger or equal than one when higher-curvature interactions are taken into account. Since these corrections become more relevant in the low-mass regime, this would allow the decay of extremal black holes in terms of energy and charge conservation. Evidence in this direction has been mainly given in the context of corrections to Einstein-Maxwell theory. Here we compute corrections to the charge-to-mass ratio of some dyonic extremal black holes explicitly embedded in the heterotic string effective theory. We find that modifications of the extremality bound depend on the solution considered, with the charge-to-mass ratio remaining unchanged or deviating positively from one. Additionally, we observe that the introduction of the higher-curvature terms increases the Wald entropy in all cases considered, whose variation does not seem to be correlated with the charge-to-mass ratio, contrary to the situation in Einstein-Maxwell theory.
|
hep-th/9207031
| null |
M.D. Freeman, K. Hornfeck and P. West
|
Commuting quantities and exceptional W-algebras
|
27 pages, KCL-TH-92-1
|
Int.J.Mod.Phys. A8 (1993) 909-928
|
10.1142/S0217751X93000357
| null |
hep-th
| null |
Sets of commuting charges constructed from the current of a U(1) Kac-Moody
algebra are found. There exists a set S_n of such charges for each positive
integer n > 1; the corresponding value of the central charge in the
Feigin-Fuchs realization of the stress tensor is c = 13-6n-6/n. The charges in
each series can be written in terms of the generators of an exceptional
W-algebra.
|
[
{
"created": "Fri, 10 Jul 1992 07:28:00 GMT",
"version": "v1"
}
] |
2015-06-26
|
[
[
"Freeman",
"M. D.",
""
],
[
"Hornfeck",
"K.",
""
],
[
"West",
"P.",
""
]
] |
Sets of commuting charges constructed from the current of a U(1) Kac-Moody algebra are found. There exists a set S_n of such charges for each positive integer n > 1; the corresponding value of the central charge in the Feigin-Fuchs realization of the stress tensor is c = 13-6n-6/n. The charges in each series can be written in terms of the generators of an exceptional W-algebra.
|
1311.6253
|
Filippo Guarnieri
|
Dario Benedetti, Filippo Guarnieri
|
One-loop renormalization in a toy model of Horava-Lifshitz gravity
|
18 pages. v2: corrected some misprints, added 3 references, some
clarifying comments and a new appendix
|
JHEP 1403 (2014) 078
|
10.1007/JHEP03(2014)078
|
AEI-2013-264
|
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We present a one loop calculation in the context of Horava-Lifshitz gravity.
Due to the complexity of the calculation in the full theory we focus here on
the study of a toy model, namely the conformal reduction of the z=2 projectable
theory in 2+1 dimensions. For this value of the dimension there are no
gravitons, hence the conformal mode is the only physical degree of freedom, and
thus we expect our toy model to lead to qualitatively correct answers regarding
the perturbative renormalization of the full theory. We find that Newton's
constant (dimensionless in Horava-Lifshitz gravity) is asymptotically free.
However, the DeWitt supermetric approaches its Weyl invariant form with the
same speed and the effective interaction coupling remains constant along the
flow. In other words, the would-be asymptotic freedom associated to the running
Newton's constant is exactly balanced by the strong coupling of the scalar mode
as the Weyl invariant limit is approached. We conclude that in such model the
UV limit is singular at one loop order, and we argue that a similar phenomenon
can be expected in the full theory, even in higher dimensions.
|
[
{
"created": "Mon, 25 Nov 2013 10:38:00 GMT",
"version": "v1"
},
{
"created": "Tue, 11 Mar 2014 09:14:02 GMT",
"version": "v2"
}
] |
2014-03-25
|
[
[
"Benedetti",
"Dario",
""
],
[
"Guarnieri",
"Filippo",
""
]
] |
We present a one loop calculation in the context of Horava-Lifshitz gravity. Due to the complexity of the calculation in the full theory we focus here on the study of a toy model, namely the conformal reduction of the z=2 projectable theory in 2+1 dimensions. For this value of the dimension there are no gravitons, hence the conformal mode is the only physical degree of freedom, and thus we expect our toy model to lead to qualitatively correct answers regarding the perturbative renormalization of the full theory. We find that Newton's constant (dimensionless in Horava-Lifshitz gravity) is asymptotically free. However, the DeWitt supermetric approaches its Weyl invariant form with the same speed and the effective interaction coupling remains constant along the flow. In other words, the would-be asymptotic freedom associated to the running Newton's constant is exactly balanced by the strong coupling of the scalar mode as the Weyl invariant limit is approached. We conclude that in such model the UV limit is singular at one loop order, and we argue that a similar phenomenon can be expected in the full theory, even in higher dimensions.
|
hep-th/9306081
|
Laurent Houart
|
Laurent Houart
|
Matrix Models and Integrable C<1 Open String Theories
|
4 pages(LaTex),ULB-TH-06/93
|
Int.J.Mod.Phys.D3:203-206,1994
|
10.1142/S0218271894000290
| null |
hep-th
| null |
No change at all but this time is possible to typset it!.
|
[
{
"created": "Thu, 17 Jun 1993 15:50:23 GMT",
"version": "v1"
},
{
"created": "Mon, 21 Jun 1993 16:00:06 GMT",
"version": "v2"
}
] |
2010-11-01
|
[
[
"Houart",
"Laurent",
""
]
] |
No change at all but this time is possible to typset it!.
|
1312.2766
|
Nicholas Halmagyi
|
Alessandra Gnecchi and Nick Halmagyi
|
Supersymmetric Black Holes in AdS4 from Very Special Geometry
|
22 pages
| null |
10.1007/JHEP04(2014)173
|
SPIN-13/22, ITP-UU-13/30
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Supersymmetric black holes in AdS spacetime are inherently interesting for
the AdS/CFT correspondence. Within a four dimensional gauged supergravity
theory coupled to vector multiplets, the only analytic solutions for regular,
supersymmetric, static black holes in AdS4 are those in the STU-model due to
Cacciatori and Klemm. We study a class of U(1)-gauged supergravity theories
coupled to vector multiplets which have a cubic prepotential, the scalar
manifold is then a very special Kahler manifold. When the resulting very
special Kahler manifold is a homogeneous space, we find analytic solutions for
static, supersymmetric AdS4 black holes with vanishing axions. The horizon
geometries of our solutions are constant curvature Riemann surfaces of
arbitrary genus.
|
[
{
"created": "Tue, 10 Dec 2013 11:45:18 GMT",
"version": "v1"
}
] |
2015-06-18
|
[
[
"Gnecchi",
"Alessandra",
""
],
[
"Halmagyi",
"Nick",
""
]
] |
Supersymmetric black holes in AdS spacetime are inherently interesting for the AdS/CFT correspondence. Within a four dimensional gauged supergravity theory coupled to vector multiplets, the only analytic solutions for regular, supersymmetric, static black holes in AdS4 are those in the STU-model due to Cacciatori and Klemm. We study a class of U(1)-gauged supergravity theories coupled to vector multiplets which have a cubic prepotential, the scalar manifold is then a very special Kahler manifold. When the resulting very special Kahler manifold is a homogeneous space, we find analytic solutions for static, supersymmetric AdS4 black holes with vanishing axions. The horizon geometries of our solutions are constant curvature Riemann surfaces of arbitrary genus.
|
hep-th/0002259
|
Eduardo S. Tututi
|
E. s. Tututi, P. Jizba
|
One particular approach to the non-equilibrium quantum dynamics
|
5 pages, 2 figures. Published in the Proceedings of the 8th Mexican
School of Particles and Fields (VIII-EMPC), Oaxaca de Juarez, Mexico, 20-28
Nov 1998
|
AIP Conf.Proc. 490 (1999) 427-431
|
10.1063/1.1301415
| null |
hep-th
| null |
We present a particular approach to the non-equilibrium dynamics of quantum
field theory. This approach is based on the Jaynes-Gibbs principle of the
maximal entropy and its implementation, throghout the initial value data, into
the dynamical equations for Green's functions.
|
[
{
"created": "Tue, 29 Feb 2000 20:45:30 GMT",
"version": "v1"
}
] |
2009-10-31
|
[
[
"Tututi",
"E. s.",
""
],
[
"Jizba",
"P.",
""
]
] |
We present a particular approach to the non-equilibrium dynamics of quantum field theory. This approach is based on the Jaynes-Gibbs principle of the maximal entropy and its implementation, throghout the initial value data, into the dynamical equations for Green's functions.
|
hep-th/0009189
|
Kluson Josef
|
J.Kluson
|
D-Branes from N non-BPS D0-Branes
|
22 pages, corrected the third section and some typos, reference added
|
JHEP 0011 (2000) 016
|
10.1088/1126-6708/2000/11/016
| null |
hep-th
| null |
In this paper we would like to show that from N non-BPS D0-branes in type IIB
theory we can obtain all BPS and non-BPS D-branes through the tachyon
condensation in the large N limit.
|
[
{
"created": "Mon, 25 Sep 2000 04:28:07 GMT",
"version": "v1"
},
{
"created": "Mon, 2 Oct 2000 04:08:01 GMT",
"version": "v2"
}
] |
2009-10-31
|
[
[
"Kluson",
"J.",
""
]
] |
In this paper we would like to show that from N non-BPS D0-branes in type IIB theory we can obtain all BPS and non-BPS D-branes through the tachyon condensation in the large N limit.
|
1905.05765
|
Arjun Kar
|
Vijay Balasubramanian, Matthew DeCross, Arjun Kar, Onkar Parrikar
|
Quantum Complexity of Time Evolution with Chaotic Hamiltonians
|
35+11 pages, 13 figures, improved motivation of cost factors,
improved discussion of superoperator corrections
| null |
10.1007/JHEP01(2020)134
| null |
hep-th cs.CC quant-ph
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We study the quantum complexity of time evolution in large-$N$ chaotic
systems, with the SYK model as our main example. This complexity is expected to
increase linearly for exponential time prior to saturating at its maximum
value, and is related to the length of minimal geodesics on the manifold of
unitary operators that act on Hilbert space. Using the Euler-Arnold formalism,
we demonstrate that there is always a geodesic between the identity and the
time evolution operator $e^{-iHt}$ whose length grows linearly with time. This
geodesic is minimal until there is an obstruction to its minimality, after
which it can fail to be a minimum either locally or globally. We identify a
criterion - the Eigenstate Complexity Hypothesis (ECH) - which bounds the
overlap between off-diagonal energy eigenstate projectors and the $k$-local
operators of the theory, and use it to show that the linear geodesic will at
least be a local minimum for exponential time. We show numerically that the
large-$N$ SYK model (which is chaotic) satisfies ECH and thus has no local
obstructions to linear growth of complexity for exponential time, as expected
from holographic duality. In contrast, we also study the case with $N=2$
fermions (which is integrable) and find short-time linear complexity growth
followed by oscillations. Our analysis relates complexity to familiar
properties of physical theories like their spectra and the structure of energy
eigenstates and has implications for the hypothesized computational complexity
class separations PSPACE $\nsubseteq$ BQP/poly and PSPACE $\nsubseteq$
BQSUBEXP/subexp, and the "fast-forwarding" of quantum Hamiltonians.
|
[
{
"created": "Tue, 14 May 2019 18:00:00 GMT",
"version": "v1"
},
{
"created": "Fri, 11 Oct 2019 03:30:59 GMT",
"version": "v2"
},
{
"created": "Wed, 3 Jun 2020 19:40:31 GMT",
"version": "v3"
}
] |
2020-06-05
|
[
[
"Balasubramanian",
"Vijay",
""
],
[
"DeCross",
"Matthew",
""
],
[
"Kar",
"Arjun",
""
],
[
"Parrikar",
"Onkar",
""
]
] |
We study the quantum complexity of time evolution in large-$N$ chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator $e^{-iHt}$ whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion - the Eigenstate Complexity Hypothesis (ECH) - which bounds the overlap between off-diagonal energy eigenstate projectors and the $k$-local operators of the theory, and use it to show that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-$N$ SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with $N=2$ fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE $\nsubseteq$ BQP/poly and PSPACE $\nsubseteq$ BQSUBEXP/subexp, and the "fast-forwarding" of quantum Hamiltonians.
|
hep-th/9706106
|
Michail Stoilov
|
M. N. Stoilov
|
On the Connection between Pauli-Villars and Higher Derivative
Regularizations
|
9 pages, harvmac
|
Annals Phys. 7 (1998) 1-8
|
10.1002/andp.19985100102
|
INRNE-TH-97/6
|
hep-th
| null |
It is shown that in some cases higher (covariant) derivative regularization
for spinor field is equivalent to the gauge invariant Pauli-Villars one.
|
[
{
"created": "Fri, 13 Jun 1997 13:16:22 GMT",
"version": "v1"
}
] |
2015-06-26
|
[
[
"Stoilov",
"M. N.",
""
]
] |
It is shown that in some cases higher (covariant) derivative regularization for spinor field is equivalent to the gauge invariant Pauli-Villars one.
|
0905.1901
|
Jose Luis Cortes
|
J.M. Carmona, J.L. Cortes, J. Indurain, D. Mazon
|
Quantum Noncanonical Field Theory: Symmetries and Interaction
|
11 pages, minor clarifying corrections added, final version to appear
in PRD
|
Phys.Rev.D80:105014,2009
|
10.1103/PhysRevD.80.105014
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The symmetry properties of a proposal to go beyond relativistic quantum field
theory based on a modification of the commutation relations of fields are
identified. Poincar\'e invariance in an auxiliary spacetime is found in the
Lagrangian version of the path integral formulation. This invariance is
contrasted with the idea of Doubly (or Deformed) Special Relativity (DSR). This
analysis is then used to go from the free theory of a complex field to an
interacting field theory.
|
[
{
"created": "Tue, 12 May 2009 16:34:27 GMT",
"version": "v1"
},
{
"created": "Thu, 12 Nov 2009 10:36:19 GMT",
"version": "v2"
}
] |
2011-08-23
|
[
[
"Carmona",
"J. M.",
""
],
[
"Cortes",
"J. L.",
""
],
[
"Indurain",
"J.",
""
],
[
"Mazon",
"D.",
""
]
] |
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian version of the path integral formulation. This invariance is contrasted with the idea of Doubly (or Deformed) Special Relativity (DSR). This analysis is then used to go from the free theory of a complex field to an interacting field theory.
|
hep-th/9701144
|
Giovanni Amelino-Camelia
|
G. Amelino-Camelia, J. Ellis, N.E. Mavromatos, and D.V. Nanopoulos
|
On the Space-Time Uncertainty Relations of Liouville Strings and D
Branes
|
8 pages, LaTex
|
Mod.Phys.Lett.A12:2029-2036,1997
|
10.1142/S0217732397002077
|
ACT-02/97 CERN-TH/96-353 CTP-TAMU-04/97 OUTP-97-04-P
|
hep-th
| null |
Within a Liouville approach to non-critical string theory, we argue for a
non-trivial commutation relation between space and time observables, leading to
a non-zero space-time uncertainty relation $\delta x \delta t > 0$, which
vanishes in the limit of weak string coupling.
|
[
{
"created": "Mon, 27 Jan 1997 21:26:20 GMT",
"version": "v1"
}
] |
2016-09-06
|
[
[
"Amelino-Camelia",
"G.",
""
],
[
"Ellis",
"J.",
""
],
[
"Mavromatos",
"N. E.",
""
],
[
"Nanopoulos",
"D. V.",
""
]
] |
Within a Liouville approach to non-critical string theory, we argue for a non-trivial commutation relation between space and time observables, leading to a non-zero space-time uncertainty relation $\delta x \delta t > 0$, which vanishes in the limit of weak string coupling.
|
1007.5156
|
Shozo Uehara
|
Shozo Uehara
|
Dilaton coupling revisited
|
11 pages, typos corrected; small corrections
|
Prog.Theor.Phys.124:581-590,2010
|
10.1143/PTP.124.581
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We reinvestigate the dilaton coupling in the string theory, which comes from
a wrapped membrane. The ghost number anomaly associated with the string
worldsheet diffeomorphism is shown to induce the dilaton coupling.
|
[
{
"created": "Thu, 29 Jul 2010 09:09:37 GMT",
"version": "v1"
},
{
"created": "Fri, 8 Oct 2010 12:53:05 GMT",
"version": "v2"
}
] |
2011-02-03
|
[
[
"Uehara",
"Shozo",
""
]
] |
We reinvestigate the dilaton coupling in the string theory, which comes from a wrapped membrane. The ghost number anomaly associated with the string worldsheet diffeomorphism is shown to induce the dilaton coupling.
|
hep-th/0701052
|
Satoshi Yamaguchi
|
Satoshi Yamaguchi
|
Semi-classical open string corrections and symmetric Wilson loops
|
14 pages, 4 figures. v2: explanation improved. v3: argument in
section 2 is improved, result not changed
|
JHEP 0706:073,2007
|
10.1088/1126-6708/2007/06/073
| null |
hep-th
| null |
In the AdS/CFT correspondence, an AdS_2 x S^2 D3-brane with electric flux in
AdS_5 x S^5 spacetime corresponds to a circular Wilson loop in the symmetric
representation or a multiply wound one in N=4 super Yang-Mills theory. In order
to distinguish the symmetric loop and the multiply wound loop, one should see
an exponentially small correction in large 't Hooft coupling. We study
semi-classically the disk open string attached to the D3-brane. We obtain the
exponent of the term and it agrees with the result of the matrix model
calculation of the symmetric Wilson loop.
|
[
{
"created": "Sun, 7 Jan 2007 22:00:43 GMT",
"version": "v1"
},
{
"created": "Fri, 26 Jan 2007 13:35:16 GMT",
"version": "v2"
},
{
"created": "Fri, 4 May 2007 09:49:22 GMT",
"version": "v3"
}
] |
2009-11-13
|
[
[
"Yamaguchi",
"Satoshi",
""
]
] |
In the AdS/CFT correspondence, an AdS_2 x S^2 D3-brane with electric flux in AdS_5 x S^5 spacetime corresponds to a circular Wilson loop in the symmetric representation or a multiply wound one in N=4 super Yang-Mills theory. In order to distinguish the symmetric loop and the multiply wound loop, one should see an exponentially small correction in large 't Hooft coupling. We study semi-classically the disk open string attached to the D3-brane. We obtain the exponent of the term and it agrees with the result of the matrix model calculation of the symmetric Wilson loop.
|
0908.3218
|
Roberto Alejandro Santos-Silva
|
Hugo Garcia-Compean, Roberto Santos-Silva
|
Link Invariants for Flows in Higher Dimensions
|
21+1 pages, LaTeX, no figures
|
J.Math.Phys.51:063506,2010
|
10.1063/1.3427319
|
Cinvestav-Fis-55-09
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
Linking numbers in higher dimensions and their generalization including gauge
fields are studied in the context of BF theories. The linking numbers
associated to $n$-manifolds with smooth flows generated by divergence-free
p-vector fields, endowed with an invariant flow measure are computed in
different cases. They constitute invariants of smooth dynamical systems (for
non-singular flows) and generalizes previous results for the 3-dimensional
case. In particular, they generalizes to higher dimensions the Arnold's
asymptotic Hopf invariant for the three-dimensional case. This invariant is
generalized by a twisting with a non-abelian gauge connection. The computation
of the asymptotic Jones-Witten invariants for flows is naturally extended to
dimension n=2p+1. Finally we give a possible interpretation and implementation
of these issues in the context of string theory.
|
[
{
"created": "Fri, 21 Aug 2009 23:34:08 GMT",
"version": "v1"
}
] |
2014-11-20
|
[
[
"Garcia-Compean",
"Hugo",
""
],
[
"Santos-Silva",
"Roberto",
""
]
] |
Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated to $n$-manifolds with smooth flows generated by divergence-free p-vector fields, endowed with an invariant flow measure are computed in different cases. They constitute invariants of smooth dynamical systems (for non-singular flows) and generalizes previous results for the 3-dimensional case. In particular, they generalizes to higher dimensions the Arnold's asymptotic Hopf invariant for the three-dimensional case. This invariant is generalized by a twisting with a non-abelian gauge connection. The computation of the asymptotic Jones-Witten invariants for flows is naturally extended to dimension n=2p+1. Finally we give a possible interpretation and implementation of these issues in the context of string theory.
|
2009.11629
|
Kazuki Kiyoshige
|
Kazuki Kiyoshige, Takahiro Nishinaka
|
The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
|
41 pages, 1 figure; minor typos corrected, results unchanged
|
JHEP02(2021)199
|
10.1007/JHEP02(2021)199
|
OCU-PHYS 522
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We construct the chiral algebra associated with the $A_{1}$-type class
$\mathcal{S}$ theory for genus two Riemann surface without punctures. By
solving the BRST cohomology problem corresponding to a marginal gauging in four
dimensions, we find a set of chiral algebra generators that form closed OPEs.
Given the fact that they reproduce the spectrum of chiral algebra operators up
to large dimensions, we conjecture that they are the complete set of
generators. Remarkably, their OPEs are invariant under an action of $SU(2)$
which is not associated with any conserved one-form current in four dimensions.
We find that this novel $SU(2)$ strongly constrains the OPEs of non-scalar
Schur operators. For completeness, we also check the equivalence of Schur
indices computed in two S-dual descriptions with a non-vanishing flavor
fugacity turned on.
|
[
{
"created": "Thu, 24 Sep 2020 12:20:07 GMT",
"version": "v1"
},
{
"created": "Sun, 28 Feb 2021 05:46:31 GMT",
"version": "v2"
}
] |
2021-03-02
|
[
[
"Kiyoshige",
"Kazuki",
""
],
[
"Nishinaka",
"Takahiro",
""
]
] |
We construct the chiral algebra associated with the $A_{1}$-type class $\mathcal{S}$ theory for genus two Riemann surface without punctures. By solving the BRST cohomology problem corresponding to a marginal gauging in four dimensions, we find a set of chiral algebra generators that form closed OPEs. Given the fact that they reproduce the spectrum of chiral algebra operators up to large dimensions, we conjecture that they are the complete set of generators. Remarkably, their OPEs are invariant under an action of $SU(2)$ which is not associated with any conserved one-form current in four dimensions. We find that this novel $SU(2)$ strongly constrains the OPEs of non-scalar Schur operators. For completeness, we also check the equivalence of Schur indices computed in two S-dual descriptions with a non-vanishing flavor fugacity turned on.
|
2312.06611
|
Luiz Brito
|
Rafael Mancini Santos, L. C. T. Brito and Cleverson Filgueiras
|
Diamonds in Klein geometry
|
Version accepted for publication in EPJPlus
|
Eur.Phys.J.Plus 138 (2023) 12, 1079
|
10.1140/epjp/s13360-023-04731-6
| null |
hep-th cond-mat.mtrl-sci physics.app-ph
|
http://creativecommons.org/licenses/by/4.0/
|
Recently it was suggested that the Unruh effect might occur in metamaterials
at accessible Unruh temperatures. In some cases, the class of metamaterials
that may be useful for this observation has a Klein instead of a Minkowski
signature. Thus, confirmation of this effect in those materials requires more
careful analysis. In this paper, we use the path integral formulation of
Quantum Field Theory to investigate the analogous to the Unruh effect in
Kleinian geometry. We calculate the analogous of the Unruh temperature for a
scalar theory, provided we restrict the action in a convenient subspace of the
Kleinian spacetime. As a consequence, we obtain the diamond temperature for a
static observer with a finite lifetime. The result suggest metamaterials as a
possible system to observe diamond regions.
|
[
{
"created": "Wed, 22 Nov 2023 13:39:59 GMT",
"version": "v1"
}
] |
2023-12-15
|
[
[
"Santos",
"Rafael Mancini",
""
],
[
"Brito",
"L. C. T.",
""
],
[
"Filgueiras",
"Cleverson",
""
]
] |
Recently it was suggested that the Unruh effect might occur in metamaterials at accessible Unruh temperatures. In some cases, the class of metamaterials that may be useful for this observation has a Klein instead of a Minkowski signature. Thus, confirmation of this effect in those materials requires more careful analysis. In this paper, we use the path integral formulation of Quantum Field Theory to investigate the analogous to the Unruh effect in Kleinian geometry. We calculate the analogous of the Unruh temperature for a scalar theory, provided we restrict the action in a convenient subspace of the Kleinian spacetime. As a consequence, we obtain the diamond temperature for a static observer with a finite lifetime. The result suggest metamaterials as a possible system to observe diamond regions.
|
2004.10769
|
Adrien Fiorucci
|
Geoffrey Comp\`ere, Adrien Fiorucci, Romain Ruzziconi
|
The $\Lambda$-BMS$_4$ Charge Algebra
|
22 pages + 23 pages appendices, 1 figure
| null |
10.1007/JHEP10(2020)205
| null |
hep-th gr-qc
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The surface charge algebra of generic asymptotically locally (A)dS$_4$
spacetimes without matter is derived without assuming any boundary conditions.
Surface charges associated with Weyl rescalings are vanishing while the
boundary diffeomorphism charge algebra is non-trivially represented without
central extension. The $\Lambda$-BMS$_4$ charge algebra is obtained after
specifying a boundary foliation and a boundary measure. The existence of the
flat limit requires the addition of corner terms in the action and symplectic
structure that are defined from the boundary foliation and measure. The flat
limit then reproduces the BMS$_4$ charge algebra of supertranslations and
super-Lorentz transformations acting on asymptotically locally flat spacetimes.
The BMS$_4$ surface charges represent the BMS$_4$ algebra without central
extension at the corners of null infinity under the standard Dirac bracket,
which implies that the BMS$_4$ flux algebra admits no non-trivial central
extension.
|
[
{
"created": "Wed, 22 Apr 2020 18:00:16 GMT",
"version": "v1"
}
] |
2020-12-02
|
[
[
"Compère",
"Geoffrey",
""
],
[
"Fiorucci",
"Adrien",
""
],
[
"Ruzziconi",
"Romain",
""
]
] |
The surface charge algebra of generic asymptotically locally (A)dS$_4$ spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The $\Lambda$-BMS$_4$ charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat limit then reproduces the BMS$_4$ charge algebra of supertranslations and super-Lorentz transformations acting on asymptotically locally flat spacetimes. The BMS$_4$ surface charges represent the BMS$_4$ algebra without central extension at the corners of null infinity under the standard Dirac bracket, which implies that the BMS$_4$ flux algebra admits no non-trivial central extension.
|
hep-th/0201271
|
Sean A. Hartnoll
|
Sean A. Hartnoll
|
Dirac equation on a G_2 manifold
|
1+11 pages. LaTeX. Minor rewording in introduction and conclusion
|
Phys.Lett. B532 (2002) 297-304
|
10.1016/S0370-2693(02)01582-4
| null |
hep-th
| null |
We find a large family of solutions to the Dirac equation on a manifold of
$G_2$ holonomy asymptotic to a cone over $S^3 \times S^3$, including all radial
solutions. The behaviour of these solutions is studied as the manifold
developes a conical singularity. None of the solutions found are both localised
and square integrable at the origin. This result is consistent with the absence
of chiral fermions in M-theory on the conifold over $S^3\times S^3$. The
approach here is complementary to previous analyses using dualities and anomaly
cancellation.
|
[
{
"created": "Thu, 31 Jan 2002 18:23:03 GMT",
"version": "v1"
},
{
"created": "Wed, 6 Feb 2002 11:28:31 GMT",
"version": "v2"
}
] |
2009-11-07
|
[
[
"Hartnoll",
"Sean A.",
""
]
] |
We find a large family of solutions to the Dirac equation on a manifold of $G_2$ holonomy asymptotic to a cone over $S^3 \times S^3$, including all radial solutions. The behaviour of these solutions is studied as the manifold developes a conical singularity. None of the solutions found are both localised and square integrable at the origin. This result is consistent with the absence of chiral fermions in M-theory on the conifold over $S^3\times S^3$. The approach here is complementary to previous analyses using dualities and anomaly cancellation.
|
1810.12659
|
Aaron Kennon
|
Aaron Kennon
|
G$_{2}$-Manifolds and M-Theory Compactifications
| null | null | null | null |
hep-th math-ph math.DG math.MP
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
The mathematical features of a string theory compactification determine the
physics of the effective four-dimensional theory. For this reason,
understanding the mathematical structure of the possible compactification
spaces is of profound importance. It is well established that the
compactification space for M-Theory must be a seven-manifold with holonomy
$G_{2}$, but much else remains to be understood regarding how to achieve a
physically-realistic effective theory from such a compactification. Much also
remains unknown about the mathematics of these $G_{2}$-Manifolds, as they are
quite difficult to construct. This review discusses progress with regards to
both the mathematical and physical considerations surrounding spaces of
holonomy $G_{2}$. Special attention is given to the known constructions of
$G_{2}$-Manifolds and the physics of their corresponding M-Theory
compactifications.
|
[
{
"created": "Tue, 30 Oct 2018 11:17:20 GMT",
"version": "v1"
},
{
"created": "Wed, 31 Oct 2018 04:08:13 GMT",
"version": "v2"
}
] |
2018-11-01
|
[
[
"Kennon",
"Aaron",
""
]
] |
The mathematical features of a string theory compactification determine the physics of the effective four-dimensional theory. For this reason, understanding the mathematical structure of the possible compactification spaces is of profound importance. It is well established that the compactification space for M-Theory must be a seven-manifold with holonomy $G_{2}$, but much else remains to be understood regarding how to achieve a physically-realistic effective theory from such a compactification. Much also remains unknown about the mathematics of these $G_{2}$-Manifolds, as they are quite difficult to construct. This review discusses progress with regards to both the mathematical and physical considerations surrounding spaces of holonomy $G_{2}$. Special attention is given to the known constructions of $G_{2}$-Manifolds and the physics of their corresponding M-Theory compactifications.
|
hep-th/0501145
|
Boris Pioline
|
Bruno Durin (LPTHE), Boris Pioline (LPTHE, LPTENS)
|
Closed strings in Misner space: a toy model for a Big Bounce ?
|
30 pages, 3 figures, to appear in the Proceedings of the NATO ASI and
EC Summer School ``String Theory: from Gauge Interactions to Cosmology'',
Cargese, France, June 7-19, 2004
|
Proceedings of the NATO ASI and EC Summer School "String Theory:
from gauge interactions to cosmology", Cargese, France, June 7-19, 2004
(2005) 177
|
10.1007/1-4020-3733-3_8
| null |
hep-th
| null |
Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one
of the simplest examples of a cosmological singularity in string theory. In
this lecture, we review the semi-classical propagation of closed strings in
this background, with a particular emphasis on the twisted sectors of the
orbifold. Tree-level scattering amplitudes and the one-loop vacuum amplitude
are also discussed.
|
[
{
"created": "Wed, 19 Jan 2005 10:54:21 GMT",
"version": "v1"
},
{
"created": "Thu, 27 Jan 2005 17:14:53 GMT",
"version": "v2"
}
] |
2015-06-26
|
[
[
"Durin",
"Bruno",
"",
"LPTHE"
],
[
"Pioline",
"Boris",
"",
"LPTHE, LPTENS"
]
] |
Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one of the simplest examples of a cosmological singularity in string theory. In this lecture, we review the semi-classical propagation of closed strings in this background, with a particular emphasis on the twisted sectors of the orbifold. Tree-level scattering amplitudes and the one-loop vacuum amplitude are also discussed.
|
hep-th/9311020
| null |
V.V. Mangazeev, S.M. Sergeev, Yu.G. Stroganov
|
New series of 3D lattice integrable models
|
17 pages, IHEP-93-126, Latex
|
Int. J. Mod. Phys. A9 (1994) 5517-5530
|
10.1142/S0217751X94002247
| null |
hep-th
| null |
In this paper we present a new series of 3-dimensional integrable lattice
models with $N$ colors. The case $N=2$ generalizes the elliptic model of our
previous paper. The weight functions of the models satisfy modified tetrahedron
equations with $N$ states and give a commuting family of two-layer
transfer-matrices. The dependence on the spectral parameters corresponds to the
static limit of the modified tetrahedron equations and weights are
parameterized in terms of elliptic functions. The models contain two free
parameters: elliptic modulus and additional parameter $\eta$. Also we briefly
discuss symmetry properties of weight functions of the models.
|
[
{
"created": "Wed, 3 Nov 1993 13:17:04 GMT",
"version": "v1"
}
] |
2015-06-26
|
[
[
"Mangazeev",
"V. V.",
""
],
[
"Sergeev",
"S. M.",
""
],
[
"Stroganov",
"Yu. G.",
""
]
] |
In this paper we present a new series of 3-dimensional integrable lattice models with $N$ colors. The case $N=2$ generalizes the elliptic model of our previous paper. The weight functions of the models satisfy modified tetrahedron equations with $N$ states and give a commuting family of two-layer transfer-matrices. The dependence on the spectral parameters corresponds to the static limit of the modified tetrahedron equations and weights are parameterized in terms of elliptic functions. The models contain two free parameters: elliptic modulus and additional parameter $\eta$. Also we briefly discuss symmetry properties of weight functions of the models.
|
1212.5000
|
Mans Henningson
|
Mans Henningson
|
Zero-mode dynamics in supersymmetric Yang-Mills-Chern-Simons theory
|
13 pages
| null |
10.1103/PhysRevD.87.105016
| null |
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons
term on a flat spatial two-torus in the limit when the torus becomes small. The
zero-modes of the fields then decouple from the non-zero modes and give rise to
a spectrum of states with energies that are given by multiples of the square of
the coupling constant. We discuss the determination of this low-energy
spectrum, both for simply connected gauge groups and for gauge groups of
adjoint type, with a few examples worked out in detail.
|
[
{
"created": "Thu, 20 Dec 2012 12:07:43 GMT",
"version": "v1"
}
] |
2013-05-29
|
[
[
"Henningson",
"Mans",
""
]
] |
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a spectrum of states with energies that are given by multiples of the square of the coupling constant. We discuss the determination of this low-energy spectrum, both for simply connected gauge groups and for gauge groups of adjoint type, with a few examples worked out in detail.
|
2105.11684
|
Bryan O. Larios
|
Allan Alonzo-Artiles, Ana Avilez-L\'opez, J. Lorenzo D\'iaz-Cruz and
Bryan O. Larios-L\'opez
|
The Higgs-Graviton Couplings: from Amplitudes to the Action
|
16 pages, 1 figure
| null | null | null |
hep-th hep-ph
|
http://creativecommons.org/publicdomain/zero/1.0/
|
In this paper we study the coupling of scalar (Higgs) particles ($\phi$) with
gravitons ($h$) and their possible effects. The general form of the 3-point
interaction $\phi(p) h(1)h(2)$ can be derived using the scaling behavior of the
spinor variables under the little group; the resulting vertices exhibit such
simplicity, that some simplifications should be hidden in the expressions
obtained from the extended scalar action. To investigate this, we study an
extended Einstein-Hilbert action that besides the minimal coupling, it also
includes terms of the form $\phi R^2$, $\phi R^{\mu\nu} R_{\mu\nu}$ and $\phi
R^{\mu\nu\rho\sigma} R_{\mu\nu\rho\sigma}$, as well as the term
$\epsilon_{\mu\nu \alpha\beta} \phi_5 R^{\mu\nu}_{\rho\sigma}
R^{\alpha\beta\rho\sigma}$ for the case of a pseudo-scalar ($\phi_5$). The
resulting vertices satisfy KLT-type relations, i.e., they can be written as the
square of the coupling of the Higgs with gluons. We find that the amplitude for
the Higgs decay into a pair of gravitons (on-shell) only receives a
contribution coming from the square of the Riemann tensor. Similar results are
obtained for the 3-body decay $\phi \to h h^* (\to XX)$, with an off-shell
graviton ($h^*$) that goes into the final state $XX$. One could expect that
these quadratic terms can produce new loop effects, however we find that the
new contribution from this non-minimal coupling to the graviton self-energy,
also vanishes for on-shell gravitons.
|
[
{
"created": "Tue, 25 May 2021 05:44:27 GMT",
"version": "v1"
}
] |
2021-05-26
|
[
[
"Alonzo-Artiles",
"Allan",
""
],
[
"Avilez-López",
"Ana",
""
],
[
"Díaz-Cruz",
"J. Lorenzo",
""
],
[
"Larios-López",
"Bryan O.",
""
]
] |
In this paper we study the coupling of scalar (Higgs) particles ($\phi$) with gravitons ($h$) and their possible effects. The general form of the 3-point interaction $\phi(p) h(1)h(2)$ can be derived using the scaling behavior of the spinor variables under the little group; the resulting vertices exhibit such simplicity, that some simplifications should be hidden in the expressions obtained from the extended scalar action. To investigate this, we study an extended Einstein-Hilbert action that besides the minimal coupling, it also includes terms of the form $\phi R^2$, $\phi R^{\mu\nu} R_{\mu\nu}$ and $\phi R^{\mu\nu\rho\sigma} R_{\mu\nu\rho\sigma}$, as well as the term $\epsilon_{\mu\nu \alpha\beta} \phi_5 R^{\mu\nu}_{\rho\sigma} R^{\alpha\beta\rho\sigma}$ for the case of a pseudo-scalar ($\phi_5$). The resulting vertices satisfy KLT-type relations, i.e., they can be written as the square of the coupling of the Higgs with gluons. We find that the amplitude for the Higgs decay into a pair of gravitons (on-shell) only receives a contribution coming from the square of the Riemann tensor. Similar results are obtained for the 3-body decay $\phi \to h h^* (\to XX)$, with an off-shell graviton ($h^*$) that goes into the final state $XX$. One could expect that these quadratic terms can produce new loop effects, however we find that the new contribution from this non-minimal coupling to the graviton self-energy, also vanishes for on-shell gravitons.
|
1506.03204
|
James Halverson
|
James Halverson and Washington Taylor
|
$\mathbb{P}^1$-bundle bases and the prevalence of non-Higgsable
structure in 4D F-theory models
|
51 pages + references, appendices. v2: references added
| null |
10.1007/JHEP09(2015)086
|
NSF-KITP-15-068, MIT-CTP-4677
|
hep-th
|
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
|
We explore a large class of F-theory compactifications to four dimensions. We
find evidence that gauge groups that cannot be Higgsed without breaking
supersymmetry, often accompanied by associated matter fields, are a ubiquitous
feature in the landscape of ${\cal N} = 1$ 4D F-theory constructions. In
particular, we study 4D F-theory models that arise from compactification on
threefold bases that are $\mathbb{P}^1$ bundles over certain toric surfaces.
These bases are one natural analogue to the minimal models for base surfaces
for 6D F-theory compactifications. Of the roughly 100,000 bases that we study,
only 80 are weak Fano bases in which there are no automatic singularities on
the associated elliptic Calabi-Yau fourfolds, and 98.3% of the bases have
geometrically non-Higgsable gauge factors. The $\mathbb{P}^1$-bundle threefold
bases we analyze contain a wide range of distinct surface topologies that
support geometrically non-Higgsable clusters. Many of the bases that we
consider contain $SU(3)\times SU(2)$ seven-brane clusters for generic values of
deformation moduli; we analyze the relative frequency of this combination
relative to the other four possible two-factor non-Higgsable product groups, as
well as various other features such as geometrically non-Higgsable candidates
for dark matter structure and phenomenological ($SU(2)$-charged) Higgs fields.
|
[
{
"created": "Wed, 10 Jun 2015 08:13:03 GMT",
"version": "v1"
},
{
"created": "Fri, 3 Jul 2015 20:23:38 GMT",
"version": "v2"
}
] |
2015-10-28
|
[
[
"Halverson",
"James",
""
],
[
"Taylor",
"Washington",
""
]
] |
We explore a large class of F-theory compactifications to four dimensions. We find evidence that gauge groups that cannot be Higgsed without breaking supersymmetry, often accompanied by associated matter fields, are a ubiquitous feature in the landscape of ${\cal N} = 1$ 4D F-theory constructions. In particular, we study 4D F-theory models that arise from compactification on threefold bases that are $\mathbb{P}^1$ bundles over certain toric surfaces. These bases are one natural analogue to the minimal models for base surfaces for 6D F-theory compactifications. Of the roughly 100,000 bases that we study, only 80 are weak Fano bases in which there are no automatic singularities on the associated elliptic Calabi-Yau fourfolds, and 98.3% of the bases have geometrically non-Higgsable gauge factors. The $\mathbb{P}^1$-bundle threefold bases we analyze contain a wide range of distinct surface topologies that support geometrically non-Higgsable clusters. Many of the bases that we consider contain $SU(3)\times SU(2)$ seven-brane clusters for generic values of deformation moduli; we analyze the relative frequency of this combination relative to the other four possible two-factor non-Higgsable product groups, as well as various other features such as geometrically non-Higgsable candidates for dark matter structure and phenomenological ($SU(2)$-charged) Higgs fields.
|
hep-th/0212057
|
Djordje Minic
|
Vishnu Jejjala, Robert G. Leigh and Djordje Minic
|
The Cosmological Constant and the Deconstruction of Gravity
|
LaTeX, 17 pages; references added, arguments clarified, discussion on
the scaling of entropy added
|
Phys.Lett. B556 (2003) 71-79
|
10.1016/S0370-2693(03)00101-1
|
VPI-IPPAP-02-16, CERN-TH/2002-351
|
hep-th gr-qc hep-ph
| null |
Witten has presented an argument for the vanishing of the cosmological
constant in 2+1 dimensions. This argument is crucially tied to the specific
properties of (2+1)-dimensional gravity. We argue that this reasoning can be
deconstructed to 3+1 dimensions under certain conditions. Our observation is
also tied to a possibility that there exists a well-defined UV completion of
(3+1)-dimensional gravity.
|
[
{
"created": "Wed, 4 Dec 2002 18:32:57 GMT",
"version": "v1"
},
{
"created": "Wed, 18 Dec 2002 21:57:50 GMT",
"version": "v2"
}
] |
2010-04-05
|
[
[
"Jejjala",
"Vishnu",
""
],
[
"Leigh",
"Robert G.",
""
],
[
"Minic",
"Djordje",
""
]
] |
Witten has presented an argument for the vanishing of the cosmological constant in 2+1 dimensions. This argument is crucially tied to the specific properties of (2+1)-dimensional gravity. We argue that this reasoning can be deconstructed to 3+1 dimensions under certain conditions. Our observation is also tied to a possibility that there exists a well-defined UV completion of (3+1)-dimensional gravity.
|
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