A Universal Counting of Black Hole Microstates in AdS$_4$

TL;DR

This paper establishes a universal relation between topologically twisted indices and three-sphere partition functions in 3D SCFTs, enabling counting of black hole microstates in AdS4 and revealing new supergravity solutions.

Contribution

It derives a universal formula linking SCFT indices and partition functions, and applies it to count microstates of AdS4 black holes and find new AdS2 solutions in supergravity.

Findings

Universal relation between twisted index and partition function

Counting of black hole microstates in AdS4

Discovery of new AdS2 supergravity solutions

Abstract

Many three-dimensional $\mathcal{N}=2$ SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS$_4$ magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS$_2$ solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.