The $$ \mathrm{T}\overline{\mathrm{T}} $$ perturbation and its geometric interpretation

Abstract

Abstract Starting from the recently-discovered $$ \mathrm{T}\overline{\mathrm{T}} $$ T 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 $$ \mathrm{T}\overline{\mathrm{T}} $$ T 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 ℝ3 are left invariant by the deformation. Analytic and numerical results concerning the perturbation of specific sine-Gordon soliton solutions are presented.