$T\bar T$ Deformations through BRST Symmetry

TL;DR

This paper explores the $T\bar T$ deformation via BRST symmetry, constructing a unitary map between original and deformed operators, and providing a non-perturbative definition of correlation functions.

Contribution

It introduces a BRST-based framework for understanding $T\bar T$ deformations, including a unitary dressing map and a gauge-invariant formulation of correlation functions.

Findings

Constructed a unitary dressing map for deformed operators.

Identified physical observables as BRST cohomology elements.

Reproduced known perturbative results non-perturbatively.

Abstract

We study the $T\bar T$ deformation using its formulation as a CFT coupled to two-dimensional dynamical gravity. Working within the BRST formalism, we apply the intertwiner construction of arXiv:2411.08865 to obtain a unitary "dressing" map between undeformed CFT operators and elements of the BRST cohomology of the deformed theory. We identify the resulting "dressed" operators corresponding to CFT primaries as the physical observables of the deformed theory and show that they arise from a field-dependent change of coordinates, in agreement with what is expected for the $T\bar T$ deformation. We then give a non-perturbative definition of deformed correlation functions as BRST-invariant expectation values of dressed operators in the gauge theory. Finally, we verify that our construction reproduces known structural and perturbative results.