# Precision Microstate Counting for the Entropy of Wrapped M5-branes

## TL;DR

This paper computes the large N expansion of twisted partition functions of 3d N=2 SCFTs from M5-branes on hyperbolic 3-manifolds, matching field theory results with holographic dual supergravity corrections.

## Contribution

It provides a precise large N expansion including all perturbative corrections for these partition functions, revealing finite termination of the series and matching holographic entropy and quantum corrections.

## Key findings

- Leading order N^3 matches black hole entropy.
- Perturbative expansion terminates at finite order.
- Log N terms match one-loop supergravity corrections.

## Abstract

We study the large $N$ expansion of twisted partition functions of 3d $\mathcal{N}=2$ superconformal field theories arising from $N$ M5-branes wrapped on a hyperbolic 3-manifold, $M_3$. Via the 3d-3d correspondence, the partition functions of these 3d ${\cal N}=2$ superconformal field theories are related to simple topological invariants on the 3-manifold. The partition functions can be expressed using only classical and one-loop perturbative invariants of $PSL(N,\mathbb{C})$ Chern-Simons theory around irreducible flat connections on $M_3$. Using mathematical results on the asymptotics of the invariants, we compute the twisted partition functions in the large $N$ limit including perturbative corrections to all orders in $1/N$. Surprisingly, the perturbative expansion terminates at finite order. The leading part of the partition function is of order $N^3$ and agrees with the Bekenstein-Hawking entropy of the dual black holes. The subleading part, in particular the $\log N$-terms in the field theory partition function is found to precisely match the one-loop quantum corrections in the dual eleven dimensional supergravity. The field theory results of other terms in $1/N$ provide a stringent prediction for higher order corrections in the holographic dual, which is M-theory.