From black holes to solvable irrelevant deformations and back

This is a combined review on the Kerr/CFT correspondence on the one hand and solvable irrelevant deformations of two-dimensional QFTs - specifically, the $T\bar T$ and $J\bar T$ deformations - on the other. These subjects are interconnected, since the microscopic description of general black holes can be linked to very special irrelevant deformations of two-dimensional CFTs; conversely, one may draw interesting insights into black hole microscopics from the study of the exactly solvable $T\bar T$ and $J\bar T$ deformations. The Kerr/CFT part emphasizes the conceptual challenges faced by this proposed holographic description of general extremal black holes, especially in light of recent advances indicating that the classical geometry of extremal black holes is unreliable. The review of the $T\bar T$ and $J\bar T$ deformations is self-contained and presented from a purely field-theoretical perspective. It covers core topics such as the finite-size spectrum, thermodynamics, scattering, non-perturbative definition and the holographic dictionary for these deformations. Particular emphasis is placed upon the extended symmetries of $T\bar T$ and $J\bar T$ - deformed CFTs, including the perfect match between the symmetries derived via field-theoretic methods and the asymptotic symmetries of the dual spacetimes. These symmetries are also central to understanding the precise relationship between single-trace $T\bar T$ and $J\bar T$ - deformed CFTs and three-dimensional asymptotically linear dilaton and, respectively, warped AdS backgrounds.