Supersymmetric Charge Constraints on AdS Black Holes from Free Fields

TL;DR

This paper demonstrates that supersymmetric charge constraints for AdS black holes can be derived from free field computations in the dual CFT, revealing a universal relation across various dimensions and hinting at a microscopic understanding beyond supersymmetric indices.

Contribution

It establishes a correspondence between nonlinear charge relations of AdS black holes and free CFT calculations, extending previous results to multiple dimensions.

Findings

Charge constraints match free CFT computations

Interactions rescale charges uniformly

Results apply to AdS4, AdS5, AdS7 black holes

Abstract

Supersymmetric AdS black hole solutions exist only when their angular momenta and charges satisfy a certain constraint that depends on the dimension. We show that these nonlinear relations on the conserved charges agree with a computation in the dual supersymmetric CFT in its free limit, with interactions entering only through a uniform rescaling of all charges. Our computations apply to the highly non-trivial charge constraints for AdS$_4$, AdS$_5$ and AdS$_7$ black holes, and generalize an earlier one for the analogous constraint in AdS$_3$. Our results suggest a microscopic understanding of AdS black holes beyond the scope of supersymmetric indices.