Black hole microstate counting in Type IIB from 5d SCFTs

We use recently established AdS${}_6$/CFT${}_5$ dualities to count the microstates of magnetically charged AdS${}_6\times S^2\times \mathrm{\Sigma }$ black holes in Type IIB. The near-horizon limit is described by solutions with AdS$2 \times \Sigma{\mathfrak{g}1} \times \Sigma{\mathfrak{g}2} \times S^2 \times \Sigma$geometry,where$\Sigma{\mathfrak{g}_i}$ are Riemann surfaces of constant curvature and $\mathrm{\Sigma }$ is a further Riemann surface over which the geometry is warped. Our results show that the topologically twisted indices of the proposed dual superconformal field theories precisely reproduce the Bekenstein-Hawking entropy of this class of black holes. This provides further support for a prescription to compute five-dimensional topologically twisted indices put forth recently, and for the proposed dualities. We confirm the $N^4$ scaling found in the sphere partition functions and extend previous matches of sphere partition functions to AdS${}_6$ solutions with monodromy.