Quantum black hole cohomologies

Microstates of BPS AdS black holes have been studied from the classical cohomologies of the maximal super-Yang-Mills theories, but their quantum natures have been conjectural. It was recently found that a classical black hole (fortuitous) cohomology in the $SO(7)$ theory is lifted by 1-loop corrections. We show that such lifts also happen in the $SU(2)$ theory, presenting both lifted/unlifted examples. In particular, the lightest fortuitous cohomology and its hairy' versions are unlifted, while many heavier core’ fortuitous ones are lifted. We argue that the entropy of classical cohomologies in the Cardy limit is larger than the indicial entropy of strictly protected states by at least $\approx 1.2\mathrm{\%}$.