High-Temperature Expansion of Supersymmetric Partition Functions

Understand

Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature ($\beta\rightarrow{0}$) behavior of supersymmetric partition functions $Z^{SUSY}(\beta)$.

• 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 $\ln Z^{SUSY}(\beta)$ terminates at order $\beta^0$.
• We also demonstrate how their formula must be modified when applied to SU($N$) toric quiver gauge theories in the planar ($N\rightarrow\infty$) limit.