Towards quantum black hole microstates

TL;DR

This work advances the microscopic understanding of black hole microstates in AdS/CFT by analyzing the cohomology of local 1/16-BPS operators in N=4 SYM. It develops a framework separating finite-N graviton cohomologies from non-graviton, black-hole-like cohomologies, and demonstrates this in the SU(2) BMN sector where an infinite tower of core primaries O_n is constructed. The index analysis reveals partial no-hair, with only a subset of graviton states capable of dressing the core states, and suggests the necessity of additional core primaries by higher charge orders, signaling a rich structure of quantum black hole microstates at finite N. The work also connects these cohomological results to hairy black hole physics, offering a bridge between field-theory cohomology and gravitational hair in AdS$_5 imes S^5$ and outlining directions to generalize to larger N and other SCFTs.

Abstract

We study the cohomology of local BPS operators in $\mathcal{N}=4$ Yang-Mills theory. The finite $N$ cohomologies consist of the graviton part (subject to the stringy exclusion principle) and the rest which may describe black hole microstates in quantum AdS/CFT. We construct an infinite tower of non-graviton cohomologies in the $SU(2)$ theory and study to what extent they simulate quantum black holes. We find signals for partial no-hair behaviors by showing that certain gravitons are forbidden to dress these cohomologies. This is in qualitative agreement with the perturbative hairs allowed around black holes, which also leads us to a natural setup to construct hairy BPS black holes. The cohomologies are simpler to study in the BMN matrix model truncation of the classical field theory.