Large $N$ Topologically Twisted Indices, Holography, and Black Holes

TL;DR

This paper derives a closed-form expression for the topologically twisted index of ABJM theory, providing insights into holography and black hole entropy by analyzing the index's behavior at large N and fixed genus.

Contribution

It introduces a simple closed-form expression for the topologically twisted index of ABJM theory valid at fixed k and all orders in 1/N, with implications for holography.

Findings

Analytic expressions for the index at fixed genus and all orders in 1/√λ

Implications for microscopic entropy counting of AdS4 black holes

Extensions to other M2-brane SCFTs discussed

Abstract

We present a simple closed form expression for the topologically twisted index of the ABJM theory as a function of the magnetic fluxes and complex chemical potentials valid at fixed $k$ and to all orders in the $1/N$ expansion. This in turn leads to analytic expressions for the topologically twisted index at fixed genus in the 't Hooft limit to all orders in the $1/\sqrt{\lambda}$ expansion. These results have important implications for holography and the microscopic entropy counting of supersymmetric static AdS$_4$ black holes. Generalizations to other SCFTs arising from M2-branes are also briefly discussed.