$T\bar T$ Deformations through BRST Symmetry

TL;DR

This work develops a BRST-based framework for $T\bar{T}$ deformations by coupling a CFT to two-dimensional dynamical gravity and employing an intertwiner $\Omega$ to map undeformed BRST cohomology $H(\mathcal{Q}_0)$ to the deformed cohomology $H(\mathcal{Q})$. The dressed CFT primaries $\mathcal{O}^{\Omega}$ are identified as physical observables of the deformed theory, corresponding to a field-dependent coordinate transformation of the original operators. Deformed correlators are defined non-perturbatively as BRST-invariant expectation values of these dressed observables, and the formalism reproduces known perturbative results while providing a non-perturbative definition that could enable deeper non-perturbative insights. The approach is extended to $J\bar{J}$ deformations and lays groundwork for potential bootstrap-type analyses, highlighting the role of gauge invariance and the emergent $ISO(1,1)$ symmetry in the deformed theory.

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.

Figures (1)

• Figure 1: Contour $\gamma(\tau)$ around the slice ${\rm Re}\,\!(z)=\tau$; the black dot represents the pole at $z=w_\tau$.