We study the index of N = 4 Yang-Mills theory on S 3 × 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.

No abstract

We study the superconformal index of 6d SCFTs from their ’t Hooft anomalies. In the Cardy limit where the angular momenta on S5 are large, we show that the leading free energy, as well as a few subleading corrections, can be computed from the 6d anomaly polynomials. Our large N free energy accounts for the entropy of supersymmetric black holes in dual AdS7.

We study M5-branes compactified on S 1 from the D0-D4 Witten index in the Coulomb phase. We first show that the prepotential of this index is S-dual, up to a simple anomalous part. This is an extension of the well-known S-duality of the 4d N = 4 theory to the 6d (2, 0) theory on finite T 2 . Using this anomalous S-duality, we find that the asymptotic free energy scales like N 3 when various temperature-like parameters are large. This shows that the number of 5d Kaluza-Klein fields for light D0-brane bound states is proportional to N 3 . We also compute some part of the asymptotic free energy from 6d chiral anomalies, which precisely agrees with our D0-D4 calculus.

No abstract