Microstate counting of AdS hyperbolic black hole entropy via the topologically twisted index.

We compute the topologically twisted index for general $$ \mathcal{N}=2 $$ supersymmetric field theories on $$ {\mathrm{\mathbb{H}}}_2\times {S}^1 $$ . We also discuss asymptotically AdS 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 ABJ M theories. [ABSTRACT FROM AUTHOR]