A 4d N=1 Cardy Formula

We study the asymptotic behavior of the (modified) superconformal index for 4d N = 1 gauge theory. By considering complexified chemical potential, we find that the 'high-temperature limit' of the index can be written in terms of the conformal anomalies 3c - 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study N = 1 theories that are dual to AdS(5) x Y-p,Y-p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

Automated summary

This study examines the asymptotic behavior of the (modified) superconformal index for 4d N = 1 gauge theory, finding that the 'high-temperature limit' of the index can be expressed in terms of conformal anomalies. Moreover, the macroscopic entropy of the interacting SCFT system is derived from the asymptotic free energy when certain bounds are satisfied. Additionally, the Carby limit of the index for N = 1 theories dual to AdS(5) x Y-p,Y-p is found to explain the Bekenstein-Hawking entropy of large black holes.