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 $\mathcal{N}=2$ gauge theories on a curved $S^2$-fibered background with complex fields, treating ABJM as a concrete example. In the Cardy and large-$N$ limits, the ABJM free energy reproduces the entropy function of rotating, electrically charged AdS$_4$ black holes, providing a microscopic derivation of the Bekenstein–Hawking entropy. The work extends localization techniques to complex backgrounds with anti-periodic Killing spinors, revealing a universal matrix-model structure that connects field theory partition functions with gravitational entropy across different approaches. It also opens avenues for computing subleading corrections and exploring broader classes of AdS/CFT black holes beyond the ABJM setup.

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.