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

TL;DR

We establish a holographic interpretation of theirrelevant but UV-complete $J\bar{T}$ deformation by showing the dual bulk remains locally AdS$_3$ with mixed boundary conditions that couple the metric to the U(1) Chern-Simons field. Using a double-trace (canonical) transformation, we derive the deformed sources and expectation values and verify them by matching black-hole thermodynamics and the deformed spectrum, first for $k=0$ and then, under a principled assumption about the current, for $k\neq 0$. The asymptotic symmetry analysis demonstrates an infinite-dimensional enhancement to Virasoro $\times$ Virasoro $\times$ Kač-Moody, with the right-moving Virasoro action becoming state-dependent and effectively non-local. Collectively, these results provide a concrete holographic framework for computing correlators in the deformed theory and shed light on UV completeness, current algebras, and non-local symmetries in holography, with potential links to warped CFTs and $T\bar{T}$-type deformations.

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 $U(1)$ Kač-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.