Heating up holography for single-trace $J\bar{T}$ deformations

TL;DR

This work strengthens the holographic link between string theory on warped AdS$_3$ backgrounds and single-trace $J\bar{T}$-deformed CFTs by extending to finite temperature. It combines worldsheet marginal deformations (via TsT) and supergravity analyses of warped BTZ, showing that the finite-temperature string spectrum, Noether charges, and entropy precisely reproduce the $J\bar{T}$-deformed CFT data. A consistent dictionary between bulk Noether charges, twisted boundary conditions, and deformed CFT quantum numbers is established, including a carefully chosen holographic $U(1)$ charge and spectral-flow parameters. The results indicate that warped BTZ and its global AdS analogue provide robust, solvable holographic laboratories for studying solvable irrelevant deformations and their thermodynamics with potential extensions to Kerr/CFT contexts.

Abstract

We study thermodynamic aspects of a tractable toy model of holography for extremal Kerr black holes proposed in [arXiv:1806.10127]. On the gravity side, the theory can be described by the worldsheet action of string theory on a warped AdS$_3$ background supported by NS-NS flux. Once we turn on temperature, the deformed background is described by a black string solution of type IIB supergravity that features a locally warped AdS$_3$ factor. The dual field theory is conjectured to be a single-trace version of a $J\bar{T}$-deformed CFT at finite temperature. As evidence for the correspondence we show that the spectrum of strings winding on the deformed background agrees with the spectrum of $J\bar{T}$-deformed CFTs. Furthermore, we show that the gravitational charges of the black string match the averaged charges of a thermal ensemble in the dual field theory. Finally, we reproduce the Bekenstein-Hawking entropy of the black string from the microscopic density of states of $J\bar{T}$-deformed CFTs.