Rotating black hole entropy from M5-branes
Francesco Benini, Dongmin Gang, Leopoldo A. Pando Zayas
Abstract
A bstract We compute the superconformal index of 3d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 2 superconformal field theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence, we use perturbative invariants of SL( N, 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. We propose a 3d-3d formulation for the refined topologically twisted index, and provide strong evidence in support of its vanishing — which agrees with the fact that the expected dual rotating magnetically-charged black hole does not exist. This provides an interesting link between gravity and a tantalizing mathematical result.