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 where the effective potential is not positive semidefinite, themore »
 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:
 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. Tue .
"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
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Works referencing / citing this record:
Cardylike asymptotics of the 4d N = 4 $$ \mathcal{N}=4 $$ index and AdS5 blackholes
journal, June 2019
 Ardehali, Arash Arabi
 Journal of High Energy Physics, Vol. 2019, Issue 6
Cardylike asymptotics of the 4d N = 4 $$ \mathcal{N}=4 $$ index and AdS5 blackholes
journal, June 2019
 Ardehali, Arash Arabi
 Journal of High Energy Physics, Vol. 2019, Issue 6