High-Temperature Expansion of Supersymmetric Partition Functions

2015/02/28 by Arash Arabi Ardehali, James T. Liu, Phillip Szepietowski · 1 citation
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1007/jhep07(2015)113

published as JHEP 1507 (2015) 113 · 15 pages plus appendices; v2: minor modifications and a "Note added"; v3: presentation improved and minor errors in app B corrected

arxiv created 2015/07/07 · arxiv updated 2015/11/13

Abstract

Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature (β→0) behavior of supersymmetric partition functions Z^SUSY(β). Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular, we see that the high-temperature expansion of ln Z^SUSY(β) terminates at order β⁰. We also demonstrate how their formula must be modified when applied to SU(N) toric quiver gauge theories in the planar (N→∞) limit. Our method for regularizing the one-loop determinants of chiral and vector multiplets helps to clarify the relation between the 4d N = 1 superconformal index and its corresponding supersymmetric partition function obtained by path-integration.

Cited by

• High-temperature asymptotics of the 4d superconformal index

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