Large AdS black holes from QFT

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.

55 pages, 7 figures; v2, v3: minor correction