A 4d N=1 Cardy Formula

Abstract

We study the asymptotic behavior of the (modified) superconformal index for 4d $\mathcal{N}=1$ 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 $\mathcal{N}=1$ theories that are dual to AdS${}_5\times Y^{p,p}$ and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

31 pages, 51 figures, v2: minor corrections, reference added

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• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes
• Off-shell phase diagram of BPS black holes in AdS${}_5$