The large $N$ limit of topologically twisted indices: a direct approach

TL;DR

This paper performs a direct saddle point analysis of the large $N$ limit of the topologically twisted index in 3D $ abla=2$ gauge theories, confirming its agreement with supergravity predictions for black hole entropy.

Contribution

It introduces a direct saddle point approach to analyze the large $N$ behavior of the index, explicitly identifying flux distributions and matching supergravity results.

Findings

Index exhibits a large $N$ factorized form.

Reproduces the entropy of magnetically charged rotating AdS$_4$ black holes.

Explicit flux distribution at large $N$.

Abstract

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.