Large AdS black holes from QFT

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.