Abstract
Starting from the recently-discovered 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 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.
Highlights
Property is a basic requirement for any sensible theory of gravity but in the current case it naturally emerges, non perturbatively and at full quantum level, from a specific irrelevant perturbation of Lorentz-invariant Quantum Field Theories (QFTs)
An important link with JT topological gravity was noticed and studied in [18], where it was shown that JT gravity coupled to matter leads to a scattering phase matching that associated to the TTperturbation [1, 2, 4,5,6, 19,20,21]
First of all, according to [18, 23], these systems should correspond to JT gravity coupled to non-topological matter, a fact that is by no mean evident from the Lagrangian point of view
Summary
It is an established fact that integrable equations in two dimensions admit an interpretation in terms of surfaces embedded inside an N -dimensional space. The two oldest examples of this connection, dating back to the works of 19th century geometers [40, 41], are the sine-Gordon and Liouville equations They appear as the Gauss-Mainardi-Codazzi (GMC) system of equations (A.14) for, respectively, pseudo-spherical and minimal surfaces embedded in the Euclidean space R3. As proved by Bonnet [42], any surface embedded in R3 is uniquely determined (up to its position in the ambient space) by two rank 2 symmetric tensors: the metric gμν (A.4) and the second fundamental tensor dμν (A.6). Their intuitive role is to measure, respectively, the length of an infinitesimal curve and the displacement of its endpoint from the tangent plane at the starting point.
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