Large AdS black holes from QFT

TL;DR

This paper analyzes the index of $ olinebreak$N=4 Yang-Mills theory at large angular momenta, revealing a microscopic origin for the entropy of supersymmetric AdS$_5$ black holes and exploring related black hole solutions.

Contribution

It provides a free QFT derivation of the black hole entropy from the index, including a generalized Cardy limit and analysis of small and large black holes in various AdS backgrounds.

Findings

Index saturates Bekenstein-Hawking entropy of known black holes

Establishes a lower bound on black hole entropy from the index

Explores new black hole solutions and their microstates

Abstract

We study the index of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$ at large angular momenta. A generalized Cardy limit exhibits macroscopic entropy at large $N$. Our result is derived using free QFT analysis, and also a background field method on $S^3$. The index sets a lower bound on the entropy. It saturates the Bekenstein-Hawking entropy of known supersymmetric AdS$_5$ black holes, thus accounting for their microstates. We further analyze the so-called Macdonald index, exploring small black holes and possibly new black holes reminiscent of hairy black holes. Finally, we study aspects of large supersymmetric AdS$_7$ black holes, using background field method on $S^5$ and 't Hooft anomalies.