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

TL;DR

This paper explores a string theory model of Kerr/CFT correspondence, introducing a $Tar{J}$-like deformation that results in null warped AdS$_3$, and analyzes the spectrum of the deformed theory.

Contribution

It proposes a single trace $Tar{J}$-like deformation in string theory on AdS$_3 imes S^3$, connecting it to null warped AdS$_3$ and analyzing its spectrum.

Findings

Deformation is marginal on the worldsheet.

Target spacetime becomes null warped AdS$_3$ after deformation.

Spectrum matches $Tar{J}$-deformed CFT predictions.

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.