The holographic interpretation of $J \bar T$-deformed CFTs

TL;DR

This paper explores the holographic dual of a $J ar T$-deformed CFT, revealing a modified AdS$_3$ spacetime with boundary conditions that encode the deformation and reproduce the deformed spectrum and thermodynamics.

Contribution

It provides a holographic interpretation of the $J ar T$ deformation, showing how it modifies boundary conditions and asymptotic symmetries in AdS$_3$ and reproduces the deformed field theory spectrum.

Findings

Modified boundary conditions mix metric and gauge fields.

Reproduction of deformed spectrum and thermodynamics.

Asymptotic symmetry group remains Virasoro and Kač-Moody.

Abstract

Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator $J \bar T$, where $J$ is a chiral $U(1)$ current and $\bar T$ is a component of the stress tensor. Assuming the original CFT was a holographic CFT, we work out the holographic dual of its $J \bar T$ deformation. We find that the dual spacetime is still AdS$_3$, but with modified boundary conditions that mix the metric and the Chern-Simons gauge field dual to the $U(1)$ current. We show that when the coefficient of the chiral anomaly for $J$ vanishes, the energy and thermodynamics of black holes obeying these modified boundary conditions precisely reproduce the previously derived field theory spectrum and thermodynamics. Our proposed holographic dictionary can also reproduce the field-theoretical spectrum in presence of the chiral anomaly, upon a certain assumption that we justify. The asymptotic symmetry group associated to these boundary conditions consists of two copies of the Virasoro and one copy of the $U(1)$ Ka\v{c}-Moody algebra, just as before the deformation; the only effect of the latter is to modify the spacetime dependence of the right-moving Virasoro generators, whose action becomes state-dependent and effectively non-local.