scholarly journals Deformations of JT gravity via topological gravity and applications

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Stefan Förste ◽  
Hans Jockers ◽  
Joshua Kames-King ◽  
Alexandros Kanargias
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Form Factors ◽  
Temperature Limit ◽  
Partition Functions ◽  
De Sitter ◽  
Spectral Form ◽  
Kdv Hierarchy ◽  
Topological Gravity ◽  
Perturbative Corrections

Abstract We study the duality between JT gravity and the double-scaled matrix model including their respective deformations. For these deformed theories we relate the thermal partition function to the generating function of topological gravity correlators that are determined as solutions to the KdV hierarchy. We specialise to those deformations of JT gravity coupled to a gas of defects, which conforms with known results in the literature. We express the (asymptotic) thermal partition functions in a low temperature limit, in which non-perturbative corrections are suppressed and the thermal partition function becomes exact. In this limit we demonstrate that there is a Hawking-Page phase transition between connected and disconnected surfaces for this instance of JT gravity with a transition temperature affected by the presence of defects. Furthermore, the calculated spectral form factors show the qualitative behaviour expected for a Hawking-Page phase transition. The considered deformations cause the ramp to be shifted along the real time axis. Finally, we comment on recent results related to conical Weil-Petersson volumes and the analytic continuation to two-dimensional de Sitter space.

scholarly journals Generalised partition functions: inferences on phase space distributions

2016 ◽  
Vol 34 (6) ◽  
pp. 557-564 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Bessel Functions ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Large Temperature ◽  
Partition Functions ◽  
Functional Dependencies ◽  
Boltzmann Factor ◽  
Nonextensive Statistical Mechanics

Abstract. It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel–Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs–Boltzmann partition function is fundamental not only to Gibbs–Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

scholarly journals AdS one-loop partition functions from bulk and edge characters

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Zimo Sun
Keyword(s):  
Partition Function ◽  
Integral Representation ◽  
Integral Transform ◽  
Integral Formula ◽  
Partition Functions ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Higher Spin ◽  
The One

Abstract We show that the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss the relation between the character integral representation and the Rindler-AdS thermal partition function.

scholarly journals Partition functions of p-forms from Harish-Chandra characters

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Justin R. David ◽  
Jyotirmoy Mukherjee
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Integral Representation ◽  
Integral Transform ◽  
Entanglement Entropy ◽  
Integral Transforms ◽  
Partition Functions ◽  
De Sitter ◽  
Symmetric Tensors ◽  
Hyperbolic Cylinders

Abstract We show that the determinant of the co-exact p-form on spheres and anti-de Sitter spaces can be written as an integral transform of bulk and edge Harish-Chandra characters. The edge character of a co-exact p-form contains characters of anti-symmetric tensors of rank lower to p all the way to the zero-form. Using this result we evaluate the partition function of p-forms and demonstrate that they obey known properties under Hodge duality. We show that the partition function of conformal forms in even d + 1 dimensions, on hyperbolic cylinders can be written as integral transforms involving only the bulk characters. This supports earlier observations that entanglement entropy evaluated using partition functions on hyperbolic cylinders do not contain contributions from the edge modes. For conformal coupled scalars we demonstrate that the character integral representation of the free energy on hyperbolic cylinders and branched spheres coincide. Finally we propose a character integral representation for the partition function of p-forms on branched spheres.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Modular invariance in finite temperature Casimir effect

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich
Keyword(s):  
Partition Function ◽  
Chemical Potential ◽  
Casimir Effect ◽  
Temperature Inversion ◽  
Massless Scalar ◽  
Partition Functions ◽  
Parallel Plates ◽  
Modular Transformations ◽  
Real Analytic ◽  
Set Up

Abstract The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell’s theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

The thermodynamics of the divalent metal fluorides. I. Heat capacity of lead tetrafluorostannate, PbSnF4, from 10.3 to 352 K

1988 ◽  
Vol 66 (4) ◽  
pp. 549-552 ◽  
Author(s):  
Jane E. Callanan ◽  
Ron D. Weir ◽  
Edgar F. Westrum Jr.
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Thermodynamic Functions ◽  
Adiabatic Calorimetry ◽  
Temperature Limit ◽  
Divalent Metal ◽  
Ion Conductor ◽  
Metal Fluorides ◽  
Fast Ion Conductor ◽  
Fast Ion

We have measured the heat capacity of the fast ion conductor PbSnF4 at 10.3 < T < 352 K by adiabatic calorimetry. Our results show anomalous values in the Cp,m in the region 300 < T < 352 K. These are associated with the α–β crystallographic transition reported at 353 K. Because the upper temperature limit of our cryostat is around 354 K, it was impossible to follow the phase transition to completion. A more subtle anomaly in the Cp,m was detected between 130 and 160 K. Standard molar thermodynamic functions are presented at selected temperatures from 5 to 350 K.

Various types of holographic metal/superconductor phase transitions with dark matter sector

2016 ◽  
Vol 26 (06) ◽  
pp. 1750046
Author(s):  
Yan Peng ◽  
Tao Chen ◽  
Guohua Liu ◽  
Pengwei Ma
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Dark Matter ◽  
Phase Transitions ◽  
Transition Temperature ◽  
De Sitter ◽  
Holographic Superconductor ◽  
Black Hole Background ◽  
Critical Phase ◽  
Matter Sector

We generalize the holographic superconductor model with dark matter sector by including the Stückelberg mechanism in the four-dimensional anti-de Sitter (AdS) black hole background away from the probe limit. We study effects of the dark matter sector on the [Formula: see text]-wave scalar condensation and find that the dark matter sector affects the critical phase transition temperature and also the order of phase transitions. At last, we conclude that the dark matter sector brings richer physics in this general metal/superconductor system.

Partition-function zeros and the SU(3) deconfining phase transition

1990 ◽  
Vol 64 (26) ◽  
pp. 3107-3110 ◽  
Author(s):  
Nelson A. Alves ◽  
Bernd A. Berg ◽  
Sergiu Sanielevici
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Partition Function Zeros ◽  
Function Zeros
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