Hightemperature asymptotics of supersymmetric partition functions
Abstract
We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) Rsymmetry on Euclidean S ^{3} × S _{β} ^{1}, with S ^{3} the unitradius squashed threesphere, and β the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using the supersymmetric localization of the gauge theory pathintegral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrixintegral over the moduli space of the holonomies of the gauge fields around S _{β} ^{1}. At high temperatures (β → 0, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrixintegral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the hightemperature limit further localizes the matrixintegral to the locus of the minima of the potential. If the effective potential is positive semidefinite, the leading hightemperature asymptotics of the partition function is given by the formula of Di Pietro and Komargodski, and the subleading asymptotics is connected to the Coulomb branch dynamics on R ^{3} × S ^{1}. In theories wheremore »
 Authors:
 Univ. of Michigan, Ann Arbor, MI (United States)
 Publication Date:
 Research Org.:
 Univ. of Michigan, Ann Arbor, MI (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1326942
 Grant/Contract Number:
 SC0007859
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 7; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Matrix Models; Supersymmetric gauge theory; Supersymmetry and Duality
Citation Formats
Ardehali, Arash Arabi. Hightemperature asymptotics of supersymmetric partition functions. United States: N. p., 2016.
Web. doi:10.1007/JHEP07(2016)025.
Ardehali, Arash Arabi. Hightemperature asymptotics of supersymmetric partition functions. United States. doi:10.1007/JHEP07(2016)025.
Ardehali, Arash Arabi. 2016.
"Hightemperature asymptotics of supersymmetric partition functions". United States.
doi:10.1007/JHEP07(2016)025. https://www.osti.gov/servlets/purl/1326942.
@article{osti_1326942,
title = {Hightemperature asymptotics of supersymmetric partition functions},
author = {Ardehali, Arash Arabi},
abstractNote = {We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) Rsymmetry on Euclidean S3 × Sβ1, with S3 the unitradius squashed threesphere, and β the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using the supersymmetric localization of the gauge theory pathintegral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrixintegral over the moduli space of the holonomies of the gauge fields around Sβ1. At high temperatures (β → 0, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrixintegral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the hightemperature limit further localizes the matrixintegral to the locus of the minima of the potential. If the effective potential is positive semidefinite, the leading hightemperature asymptotics of the partition function is given by the formula of Di Pietro and Komargodski, and the subleading asymptotics is connected to the Coulomb branch dynamics on R3 × S1. In theories where the effective potential is not positive semidefinite, the Di PietroKomargodski formula needs to be modified. In particular, this modification occurs in the SU(2) theory of IntriligatorSeibergShenker, and the SO(N) theory of BrodieChoIntriligator, both believed to exhibit “misleading” anomaly matchings, and both believed to yield interacting superconformal field theories with c < a. Lastly, two new simple tests for dualities between 4d supersymmetric gauge theories emerge as byproducts of our analysis.},
doi = {10.1007/JHEP07(2016)025},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2016,
place = {United States},
year = 2016,
month = 7
}
Web of Science

Nuclear partition functions are calculated in a Fermigas approximation which accounts for continuum singleparticle orbitals. Numerical results for ironpeak nuclei with kT< or =10 MeV indicate that partition functions and mean nuclear excitation energies are nearly as large as those given by the conventional formulation, in marked contrast with previous phenomenological treatments of this problem.

Ionization Equilibrium and Partition Functions of HighTemperature Weakly Nonideal Flibe Gas
A model for the ionization equilibrium of weakly nonideal Flibe plasma is presented in terms of a set of coupled nonlinear Saha equations supplemented by electroneutrality and conservation of nuclei. Nonideality effects have been taken into account in terms of lowering of the ionization potentials and truncated partition functions. A simple formulation and solution strategy of the Saha equations for the single element case has been extended to apply for the case of plasma mixtures and has been used to calculate the composition of partially ionized Flibe plasma over a wide range of temperatures and densities. A criterion for themore » 
Partition functions of supersymmetric gauge theories in noncommutative R{sup 2D} and their unified perspective
We investigate cohomological gauge theories in noncommutative R{sup 2D}. We show that vacuum expectation values of the theories do not depend on noncommutative parameters, and the large noncommutative parameter limit is equivalent to the dimensional reduction. As a result of these facts, we show that a partition function of a cohomological theory defined in noncommutative R{sup 2D} and a partition function of a cohomological field theory in R{sup 2D+2} are equivalent if they are connected through dimensional reduction. Therefore, we find several partition functions of supersymmetric gauge theories in various dimensions are equivalent. Using this technique, we determine the partitionmore » 
Partition functions for the rigid string and membrane at any temperature
Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using [zeta]function regularization methods, the results are analytically continued and written as asymptotic sums of RiemannHurwitz [zeta] functions, which provide very good numerical approximations with just a few first terms. This allows us to obtain systematic corrections to the results of Polchinski [ital et] [ital al]., corresponding to the limits [ital T][r arrow]0 and [ital T][r arrow][infinity] of the rigid string, and to analyze the intermediate range of temperatures. In particular, a way to obtain the Hagedornmore » 
Partition functions, the Bekenstein bound and temperature inversion in antide Sitter space and its conformal boundary
We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function L=ES/(2{pi}R), where R is some measure of the size of the system. The minimum of L occurs at the temperature T=1/(2{pi}R). In the case of ndimensional antide Sitter spacetime, the rather poorly defined size R acquires a precise definition in terms of the AdS radius l, with R=l/(n2). We previously found that the Bekenstein bound holds for all known black holes in AdS. However, in this paper we show that the Bekenstein bound is not generally valid formore »