$T\bar{T}$-deformed correlators from a 2D gravity description

TL;DR

This paper explores how $T\bar{T}$-deformed correlators in 2D conformal field theories can be understood through a 2D gravity perspective, enabling finite coupling computations and extending the random geometry approach.

Contribution

It introduces a gravity-based method to compute $T\bar{T}$-deformed correlators at finite coupling, generalizing the random geometry approach and providing explicit calculations.

Findings

Computed leading logarithmic contributions to 2- and 3-point functions at all orders in coupling.

Reproduced known results and obtained new insights into $T\bar{T}$-deformed correlators.

Demonstrated the utility of a 2D gravity framework for finite coupling analysis.

Abstract

We study correlators in two-dimensional $T\bar{T}$-deformed conformal field theories by interpreting the $T\bar{T}$ deformation as a coupling to two-dimensional gravity. To demonstrate the utility of the massive gravity framework as a particular realization of the gravitational interpretation, we show how the $T\bar{T}$-deformed correlators at finite coupling can be computed by adopting a judicious parametrization of the 2D metric and a preferred choice of zweibeins. To illustrate how this method works in practice, we compute the leading logarithmic contributions to two- and three-point functions to all orders in the $T\bar{T}$ coupling, reproducing a known result while producing new findings. This framework generalizes the random geometry approach to finite coupling.