Rotating Black Hole Entropy from M5-branes

Understand

We compute the superconformal index of 3d $\mathcal{N}=2$ superconformal theories obtained from $N$ M5-branes wrapped on a hyperbolic 3-manifold.

• Exploiting the 3d-3d correspondence, we use perturbative invariants of $SL(N,\mathbb{C})$ Chern-Simons theory to determine the superconformal index in the large $N$ limit, including corrections logarithmic in $N$.
• The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS$_4$ black holes.
• We also verify that the supergravity one-loop contribution to the $\log N$ term coincides with the field theoretic result.