$T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry

TL;DR

This paper develops a geometric method to compute stress-tensor correlators in $T\bar{T}$-deformed 2D conformal field theories, revealing a logarithmic correction in four-point functions absent in lower-point correlators.

Contribution

It introduces a novel geometric approach based on random geometry to calculate stress-tensor correlators under $T\bar{T}$ deformation, including derivation of the deformed Polyakov-Liouville action.

Findings

Derived first-order $T\bar{T}$-deformed stress-tensor correlators

Confirmed results with conformal perturbation theory

Discovered logarithmic corrections in four-point functions

Abstract

We study stress-tensor correlators in the $T\bar{T}$-deformed conformal field theories in two dimensions. Using the random geometry approach to the $T\bar{T}$ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $T\bar{T}$ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $T\bar{T}$ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check consistency with the $T\bar{T}$-deformed operator product expansions of the stress tensor. A salient feature of the $T\bar{T}$-deformed stress-tensor correlators is a logarithmic correction that is absent in two and three-point functions but starts appearing in a four-point function.