Finite N black hole cohomologies

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.