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

Understand

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.