$T\bar{T}$ deformed CFT as a non-critical string

TL;DR

This paper develops an exact worldsheet string theory framework for $T\bar{T}$ deformed 2D CFTs, connecting them to non-critical strings and providing explicit formulas for spectra, partition functions, and correlation functions.

Contribution

It introduces a novel worldsheet approach to $T\bar{T}$ deformed CFTs using non-critical string theory, enabling exact calculations of physical quantities.

Findings

Computed the physical spectrum and partition function matching known results.

Derived an integral formula for three-point functions and OPE coefficients.

Established a connection between $T\bar{T}$ deformations and non-critical string theory.

Abstract

We present a new exact treatment of $T\bar{T}$ deformed 2D CFT in terms of the worldsheet theory of a non-critical string. The transverse dimensions of the non-critical string are represented by the undeformed CFT, while the two longitudinal light-cone directions are described by two scalar fields $X^+$ and $X^-$ with free field OPE's but with a modified stress tensor, arranged so that the total central charge adds up to 26. The relation between our $X^\pm$ field variables and 2D dilaton gravity is indicated. We compute the physical spectrum and the partition function and find a match with known results. We describe how to compute general correlation functions and present an integral expression for the three point function, which can be viewed as an exact formula for the OPE coefficients of the $T\bar{T}$ deformed theory. We comment on the relationship with other proposed definitions of local operators.