Topologically twisted index of $T[SU(N)]$ at large $N$

TL;DR

This paper calculates the large N limit of the topologically twisted index of the 3D T[SU(N)] theory on a Riemann surface times a circle, connecting it to black hole entropy via holography.

Contribution

It provides a new large N expression for the twisted index of T[SU(N)] and links it to holographic black hole entropy using recent 5D gauge theory results.

Findings

Reproduces the universal black hole entropy from the twisted index.

Derives an explicit formula for the index at large N.

Connects 3D gauge theory results with holographic duals.

Abstract

We compute, in the large $N$ limit, the topologically twisted index of the 3d $T[SU(N)]$ theory, namely the partition function on $\Sigma_{\mathfrak{g}} \times S^1$, with a topological twist on the Riemann surface $\Sigma_{\mathfrak{g}}$. To provide an expression for this quantity, we take advantage of some recent results obtained for five dimensional quiver gauge theories. In case of a universal twist, we correctly reproduce the entropy of the universal black hole that can be embedded in the holographically dual solution.