Black hole states at finite N

We study new cohomologies for the local BPS operators of the maximal super-Yang-Mills theory to better understand the black hole microstates. We first analyze the index of these black hole operators and explicitly construct their cohomologies to study how they imitate the quantum black holes. We find many towers of states and partial no-hair behaviors where certain gravtions are forbidden to dress these black hole operators. This qualitatively agrees with the behavior of the perturbative hairy BPS black holes or the so-called grey galaxies. Throughout this talk, we mainly focus on a subsector of the field theory corresponding to the BMN matrix theory, which exhibits a black hole-like entropy growth at large N.