The $\textrm{T}\bar{\textrm{T}}$ perturbation and its geometric interpretation

TL;DR

This paper demonstrates that $ extrm{T}ar{ extrm{T}}$-perturbed classical solutions in bosonic field theories are equivalent to original solutions via a specific field-dependent coordinate change, linking to geometric and quantum gravity interpretations.

Contribution

It proves a geometric interpretation of $ extrm{T}ar{ extrm{T}}$ deformations as coordinate transformations and explores their effects on sine-Gordon solitons.

Findings

Deformed solutions are equivalent to original solutions under a coordinate change.

Sine-Gordon solitons' geometric properties are preserved under deformation.

Analytic and numerical analysis of soliton perturbations are provided.

Abstract

Starting from the recently-discovered $\textrm{T}\bar{\textrm{T}}$-perturbed Lagrangians, we prove that the deformed solutions to the classical EoMs for bosonic field theories are equivalent to the unperturbed ones but for a specific field-dependent local change of coordinates. This surprising geometric outcome is fully consistent with the identification of $\textrm{T}\bar{\textrm{T}}$-deformed 2D quantum field theories as topological JT gravity coupled to generic matter fields. Although our conclusion is valid for generic interacting potentials, it first emerged from a detailed study of the sine-Gordon model and in particular from the fact that solitonic pseudo-spherical surfaces embedded in $\mathbb R^3$ are left invariant by the deformation. Analytic and numerical results concerning the perturbation of specific sine-Gordon soliton solutions are presented.