Supersymmetric black holes and $T\bar{T}$ deformation

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.

arXiv commentv2: improved discussion

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• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• Non-trivial saddles in microscopic description of black holes
• Statistical Mechanics of Exponentially Many Low Lying States
• Moving holographic boundaries
• An extremal black hole with a unique ground state