9968 1809.09593 10.1007/JHEP02(2019)085 85 85 The T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ perturbation and its geometric interpretation Regular Article - Theoretical Physics 1 29 2019 2 14 2018 10 18 2019 1 22 2019 2 5 2019 2 14 The Author(s) 2019 13130 2019 2019 2 2 Riccardo Conti riccardo.conti@to.infn.it Stefano Negro stefano.negro@stonybrook.edu Roberto Tateo tateo@to.infn.it grid.470222.1 Dipartimento di Fisica and Arnold-Regge Center, Università di Torino and INFN, Sezione di Torino Via P. Giuria 1 I-10125 Torino Italy C.N. Yang Institute for Theoretical Physics New York Stony Brook Stony Brook NY 11794-3840 U.S.A. Abstract Starting from the recently-discovered T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -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 T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -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. Keywords Bethe Ansatz Integrable Field Theories ArXiv ePrint: 1809.09593