An extremization principle for the entropy of rotating BPS black holes in AdS5_5

We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS$_5\times S^5$ can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for $\mathcal{N}=4$ super Yang-Mills.Comment: 27 pages; v2: refs added; v3: ref adde

The large NN limit of topologically twisted indices: a direct approach

We study the large $N$ limit of the refined topologically twisted index of three-dimensional $\mathcal{N} = 2$ gauge theories with a holographic dual, which is relevant for counting the number of microstates of rotating, magnetically charged and twisted AdS$_4$ black holes. As a difference with previous computations, we perform a direct saddle point analysis of the relevant matrix model. Among other things we explicitly identify the distribution of gauge magnetic fluxes that contributes at large $N$. The index exhibits a large $N$ factorized form in agreement with the supergravity expectations based on gravitational blocks and correctly reproduces the entropy of magnetically charged rotating AdS$_4 \times S^7$ black holes.Comment: 47 pages, 4 figure