Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index

Abstract

We compute the topologically twisted index for general $\mathcal{N}=2$ supersymmetric field theories on ${\mathbb{H}}_2\times S^1$. We also discuss asymptotically $Ad{S}_4$ magnetically charged black holes with hyperbolic horizon, in four-dimensional $\mathcal{N}=2$ gauged supergravity. With certain assumptions, put forward by Benini, Hristov and Zaffaroni, we find precise agreement between the black hole entropy and the topologically twisted index, for $ABJM$ theories.

39 pp + appendices, v2: references added, typos corrected

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