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

Abstract

We use symmetries to define a new class of operators and compute their correlation functions in the $J\bar{T}$-deformed conformal field theory on the plane, following the strategy developed in [1]. The symmetry algebra of the deformed theory 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 distinct operator classes. In this paper, we focus on two types of operators: Dressed operators transform as primaries under the symmetries and depend on non-local coordinates, which involve integration over a region. Physical operators, introduced in this work, depend only on local quantities at the classical level and can be expressed in a manageable way in terms of dressed operators and currents. At the quantum level, we assume the existence of dressed operators and the Ward identities that relate them. The physical operators are then defined via the dressed operators and currents, the expression of which is a natural uplifting of the classical version. 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. In position space, the leading-log contributions to the two-point correlators are summed to all orders in the deformation parameter, revealing non-perturbative behavior.