Strings on warped AdS$_3$ via $T\bar{J}$ deformations

TL;DR

This work constructs a toy model of Kerr/CFT by embedding string theory on AdS$_3\times S^3$ and introducing a single-trace $(2,1)$ deformation, interpreted as a $T\bar{K}$-type perturbation of the dual CFT. The deformation is shown to be marginal on the worldsheet and to produce a warped AdS$_3$ geometry (null warped in the dimensionally reduced theory), realized via a TsT-like transformation. The finite-size spectrum on the cylinder is derived and shown to match the expectations from $T\bar{K}$ deformations up to a shift in the $\bar{U}(1)$ charge, with explicit expressions for $E_L(\lambda)$, $E_R(\lambda)$ and $\bar{Q}(\lambda)$ that depend on the deformation parameter $\lambda$, spectral flow $w$, and charges. Overall, the paper ties a concrete worldsheet construction to Kerr/CFT characteristics by connecting a single-trace deformation to null warped backgrounds and a tractable deformed spectrum, providing a controlled setting to study nonlocal QFTs dual to (near) extremal black holes.

Abstract

We study a toy model of the Kerr/CFT correspondence using string theory on AdS$_3 \times S^3$. We propose a single trace irrelevant deformation of the dual CFT generated by a vertex operator with spacetime dimensions (2,1). This operator shares the same quantum numbers as the integrable $T\bar{J}$ deformation of two-dimensional CFTs where $\bar{J}$ is a chiral $U(1)$ current. We show that the deformation is marginal on the worldsheet and that the target spacetime is deformed to null warped AdS$_3$ upon dimensional reduction. We also calculate the spectrum of the deformed theory on the cylinder and compare it to the field theory analysis of $T\bar{J}$-deformed CFTs.