Large $N$ Superconformal Indices for 3d Holographic SCFTs

TL;DR

This paper derives exact formulas for the superconformal index of 3d holographic SCFTs in a specific limit, revealing insights into black hole physics and extending previous results to new theories.

Contribution

It introduces a novel method connecting superconformal indices with Bethe Ansatz Equations, providing all-order results in the large N limit for multiple 3d theories.

Findings

Closed-form expressions for the superconformal index in the Cardy-like limit.

Extension of results to 3d $ ext{N}=4$ SYM with matter fields.

Implications for holography and charged black holes in AdS$_4$.

Abstract

We study a limit of the superconformal index of the ABJM theory on $S^1\times S^2$ in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the $1/N$ expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d $\mathcal{N}=4$ SYM coupled to one adjoint and $N_f$ fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in AdS$_4$.