High-Temperature Expansion of Supersymmetric Partition Functions

Feb 26, 2015
27 pages
Published in:
  • JHEP 07 (2015) 113
  • Published: Jul 22, 2015
e-Print:
Report number:
  • MCTP-15-06,
  • ITP-UU-15-03

Citations per year

201520172019202120230246810
Abstract: (Springer)
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 ZSUSY^{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 ZSUSY^{SUSY}(β) terminates at order β0^{0}. 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 \mathcal{N}=1 superconformal index and its corresponding supersymmetric partition function obtained by path-integration.
Note:
  • 15 pages plus appendices; v2: minor modifications and a "Note added"; v3: presentation improved and minor errors in app B corrected
  • Supersymmetric gauge theory
  • Anomalies in Field and String Theories
  • AdSCFT Correspondence
  • 1/N Expansion
  • multiplet: vector
  • gauge field theory: quiver
  • partition function
  • high temperature expansion
  • field theory: conformal
  • regularization