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

Abstract

Starting from the recently-discovered $\text{T}\bar{\text{T}}$-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 $\text{T}\bar{\text{T}}$-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.

v2 : Expanded version with new comments, numerical results and 16 figures added. Minor typos corrected. Extra references added. 25 pages. 4 figures v3 : JHEP version. Section 6 added. Minor typos corrected. Extra reference added. 30 pages. 5 figures