Supersymmetric black holes and $T\bar T$ deformation

TL;DR

This paper proposes that the entropy of supersymmetric black holes in string theory can be understood through a $T\bar T$ deformation of the dual two-dimensional conformal field theory, linking black hole mass to deformed energy levels.

Contribution

It introduces a novel interpretation of black hole mass as a $T\bar T$ deformed energy, connecting black hole physics with irrelevant deformations of CFTs in a precise manner.

Findings

Black hole mass matches $T\bar T$ deformed energy levels.

The $T\bar T$ parameter relates to the inverse of the black hole mass.

Implications include a Hagedorn temperature for wrapped M5-branes.

Abstract

The entropy of supersymmetric black holes in string theory compactifications can be related to that of a D- or M-brane system, which in many cases can be further reduced to a two-dimensional conformal field theory (CFT). For black holes in M-theory, this relation involves a decoupling limit where the black hole mass diverges. We suggest that moving away from this limit corresponds to a specific irrelevant perturbation of the CFT, namely the supersymmetric completion of the $T\bar T$ deformation. We demonstrate that the black hole mass matches precisely with the $T\bar T$ deformed energy levels, upon identifying the $T\bar T$ deformation parameter with the inverse of the leading term of the black hole mass. We discuss various implications for black holes and deformed CFT's, including a Hagedorn temperature for wrapped M5-branes, and potential change of degeneracies in the deformed theory.