Finite $N$ black hole cohomologies

TL;DR

This paper introduces new cohomologies for BPS operators in $ ext{SU}(3)$ and $ ext{SU}(4)$ $ ext{N}=4$ Yang-Mills theory to explore black hole microstates, revealing threshold levels, state towers, and entropy growth behaviors.

Contribution

It constructs explicit threshold cohomologies and analyzes black hole microstate structures within these gauge theories, including the BMN sector.

Findings

Identification of threshold levels for black hole operators

Construction of explicit threshold cohomology in SU(3)

Evidence of black hole-like entropy growth in the BMN sector

Abstract

We study new cohomologies for the BPS operators of the $\mathcal{N}=4$ Yang-Mills theory with $SU(3)$ and $SU(4)$ gauge groups, to better understand the black hole microstates. We first study the index of these black hole operators and identify their apparent threshold levels. For $SU(3)$, we find many towers of states and partial no-hair behaviors. We explicitly construct the threshold cohomology in the $SU(3)$ theory. We study throughout this paper a subsector of the field theory corresponding to the BMN matrix theory. We also argue that the BMN sector exhibits a black hole like entropy growth at large $N$.