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

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.

35 pages, no figures; v2: typos corrected, discussions added in Sec. 5; v3: typos corrected in Sec. 2.1, expositions improved in Sec. 2.1 and Sec. 5

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