# Black hole microstate counting in Type IIB from 5d SCFTs

## TL;DR

This paper uses AdS$_6$/CFT$_5$ dualities to count black hole microstates in Type IIB string theory, showing that dual field theory indices match the black hole entropy and confirming the $N^4$ scaling.

## Contribution

It provides a novel microstate counting method for AdS$_6$ black holes using 5d SCFT dualities and confirms the accuracy of topologically twisted indices in reproducing black hole entropy.

## Key findings

- Topologically twisted indices match Bekenstein-Hawking entropy.
- Confirmed $N^4$ scaling in black hole microstate counting.
- Extended previous sphere partition function results to AdS$_6$ solutions with monodromy.

## Abstract

We use recently established AdS$_6$/CFT$_5$ dualities to count the microstates of magnetically charged AdS$_6 \times S^2 \times \Sigma$ 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 $\Sigma$ 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.