# Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds

## TL;DR

This paper computes the twisted index of 4d class S theories on hyperbolic 3-manifolds, revealing a match with black hole entropy in AdS5 holography through topological invariants and perturbative expansions.

## Contribution

It provides a topological formula for the twisted index using analytic torsions and determines its full 1/N expansion, connecting field theory to black hole entropy.

## Key findings

- Full perturbative 1/N expansion of the twisted index
- Matching of the leading index with black hole entropy
- Expression of the index in terms of topological invariants

## Abstract

We study the twisted index of 4d $\mathcal{N}$ = 2 class S theories on a closed hyperbolic 3-manifold $M_3$. Via 6d picture, the index can be written in terms of topological invariants called analytic torsions twisted by irreducible flat connections on the 3-manifold. Using the topological expression, we determine the full perturbative 1/N expansion of the twisted index. The leading part nicely matches the Bekestein-Hawking entropy of a magnetically charged black hole in the holographic dual $AdS_5$ with $AdS_2\times M_3$ near-horizon.