Black hole microstates in AdS$_4$ from supersymmetric localization

TL;DR

This paper computes the microstate count of supersymmetric AdS$_4$ black holes using the topologically twisted index of the ABJM theory, successfully matching the black hole entropy in the large N limit.

Contribution

It demonstrates how to derive black hole microstates from a dual field theory via supersymmetric localization, providing a concrete holographic microstate counting method.

Findings

Topologically twisted index reproduces black hole entropy

Extremization determines the exact R-symmetry

Large N limit confirms the holographic correspondence

Abstract

This paper addresses a long standing problem, the counting of the microstates of supersymmetric asymptotically AdS black holes in terms of a holographically dual field theory. We focus on a class of asymptotically AdS$_4$ static black holes preserving two real supercharges which are dual to a topologically twisted deformation of the ABJM theory. We evaluate in the large $N$ limit the topologically twisted index of the ABJM theory and we show that it correctly reproduces the entropy of the AdS$_4$ black holes. An extremization of the index with respect to a set of chemical potentials is required. We interpret it as the selection of the exact R-symmetry of the superconformal quantum mechanics describing the horizon of the black hole.