skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: High-temperature asymptotics of supersymmetric partition functions

Abstract

We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) R-symmetry on Euclidean S 3 × S β 1, with S 3 the unit-radius squashed three-sphere, 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 path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral 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 matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If the effective potential is positive semi-definite, the leading high-temperature 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 » the effective potential is not positive semi-definite, the Di Pietro-Komargodski formula needs to be modified. In particular, this modification occurs in the SU(2) theory of Intriligator-Seiberg-Shenker, and the SO(N) theory of Brodie-Cho-Intriligator, 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.« less

Authors:
 [1]
  1. 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 1029-8479
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. High-temperature asymptotics of supersymmetric partition functions. United States: N. p., 2016. Web. doi:10.1007/JHEP07(2016)025.
Ardehali, Arash Arabi. High-temperature asymptotics of supersymmetric partition functions. United States. doi:10.1007/JHEP07(2016)025.
Ardehali, Arash Arabi. 2016. "High-temperature asymptotics of supersymmetric partition functions". United States. doi:10.1007/JHEP07(2016)025. https://www.osti.gov/servlets/purl/1326942.
@article{osti_1326942,
title = {High-temperature 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) R-symmetry on Euclidean S3 × Sβ1, with S3 the unit-radius squashed three-sphere, 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 path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral 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 matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If the effective potential is positive semi-definite, the leading high-temperature 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 semi-definite, the Di Pietro-Komargodski formula needs to be modified. In particular, this modification occurs in the SU(2) theory of Intriligator-Seiberg-Shenker, and the SO(N) theory of Brodie-Cho-Intriligator, 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
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3works
Citation information provided by
Web of Science

Save / Share:
  • Nuclear partition functions are calculated in a Fermi-gas approximation which accounts for continuum single-particle orbitals. Numerical results for iron-peak 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.
  • A model for the ionization equilibrium of weakly non-ideal Flibe plasma is presented in terms of a set of coupled nonlinear Saha equations supplemented by electro-neutrality and conservation of nuclei. Non-ideality 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 » validity of the assumption of local thermodynamic equilibrium is presented and applied to the result. Effects of non-ideality corrections and approximating the partition function to the statistical weight of the ground state have been quantified and presented.« less
  • 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 » function of the N=4 U(1) gauge theory in noncommutative R{sup 4}, where its action does not include a topological term. The result is common among (8-dim, N=2), (6-dim, N=2), (2-dim, N=8) and the IKKT matrix model given by their dimensional reduction to 0-dim.« less
  • 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 Riemann-Hurwitz [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 » temperature for the rigid membrane is thus found.« less
  • We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function L=E-S/(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 n-dimensional anti-de Sitter spacetime, the rather poorly defined size R acquires a precise definition in terms of the AdS radius l, with R=l/(n-2). 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 » free quantum fields in AdS, even if one includes the Casimir energy. Some other aspects of thermodynamics in anti-de Sitter spacetime are briefly touched upon.« less