Strings on warped AdS$_3$ via $Tbar{J}$ deformations

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 $Tbar{J}$ 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 $Tbar{J}$-deformed CFTs.