From black holes to solvable irrelevant deformations and back

Abstract

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.

Figures (30)

• Figure 1: The triad of properties that we will be using to characterise theories.
• Figure 2: The typical holographic situation we will consider. The non-AdS spacetime of interest is obtained via a decoupling limit and corresponds to a non-normalisable deformation of an AdS spacetime in the interior. The holographically dual picture is that of a UV-complete but non-standard theory that can be obtained via a finely-tuned irrelevant deformation of a CFT.
• Figure 3: Properties of the holographic duals to warped AdS$_3$ spacetimes embedded in string theory, inferred using bottom-up methods. If it is true that the symmetries contain a Virasoro$_R$ factor, there is a clear tension with the non-localities exhibited by correlation functions on this side.
• Figure 4: The property triad for $2d$ unitary CFTs. They all follow from global conformal invariance and locality.
• Figure 5: The triad of properties of the dual to near-extreme Kerr, as inferred via bottom-up methods.