Microscopic Entropy of Rotating Electrically Charged AdS$_4$ Black Holes from Field Theory Localization

TL;DR

This paper uses supersymmetric localization to compute the exact partition function of 3d gauge theories on a specific background, linking it to the microscopic entropy of dual AdS4 black holes.

Contribution

It provides a novel exact calculation of the partition function for 3d $ ext{N}=2$ theories on a fibered sphere background, connecting field theory results to black hole entropy.

Findings

Partition function reduces to a matrix model including monopole configurations.

Large-N limit reproduces black hole entropy in the Cardy limit.

Microscopic field theory explanation for Bekenstein-Hawking entropy.

Abstract

We employ supersymmetric localization to determine the exact partition function of 3d $\mathcal{N}=2$ gauge theories on a background given by a round $S^2$ fibered over a circle and certain complexified background fields. The Coulomb branch localization locus includes monopole configurations, and the partition function reduces to a matrix model. We consider the partition function of the ABJM theory on this background as an explicit case. We verify that the large-$N$ limit of the ABJM theory partition function produces, in the Cardy limit, the entropy function of the dual rotating, electrically charged asymptotically AdS$_4$ supersymmetric black holes and thus provides a microscopic explanation for the Bekenstein-Hawking entropy.