Symmetries, operators and correlators in $J\bar{T}$ deformed CFTs

TL;DR

This paper develops a framework for symmetry generators and operators in $Jar{T}$-deformed CFTs, enabling the computation of correlation functions that match string theory predictions and reveal instanton effects.

Contribution

It generalizes the symmetry and operator construction from $Tar{T}$ to $Jar{T}$ deformations, including non-local symmetries and non-perturbative correlator analysis.

Findings

Derived the symmetry algebra with local and non-local sectors.

Computed two- and N-point functions matching string theory.

Identified instanton contributions in position-space correlators.

Abstract

We construct symmetry generators and operators for $J\bar{T}$-deformed conformal field theories by generalizing the framework established for $T\bar{T}$ deformations. Working in the Hamiltonian formalism on the plane, we derive the symmetry algebra of the deformed theory, which consists of a local Virasoro-Kac-Moody algebra in the left-moving sector and a non-local counterpart in the right-moving sector. This algebraic structure guides the definition of two operator classes: dressed operators, which transform as primaries under the deformed symmetries, and local physical operators. While dressed operators are local only in the left null direction, physical operators maintain locality in both directions and are constructed from dressed operators and currents. This formulation allows the powerful constraints of conformal symmetry to be leveraged for computing physical observables. Consequently, we employ conformal perturbation theory to compute the two-point and $N$-point functions of physical operators. In momentum space, we sum the most UV-sensitive contributions to all orders; the results show precise agreement with string theory predictions. Furthermore, a non-perturbative analysis of the position-space correlator reveals an instanton contribution, providing a complete characterization of the correlation functions.