Soliton, breather and shockwave solutions of the Heisenberg and the T T ¯ $$ T\overline{T} $$ deformations of scalar field theories in 1+1 dimensions

A bstract In this note we study soliton, breather and shockwave solutions in certain two dimensional field theories. These include: (i) Heisenberg’s model suggested originally to describe the scattering of high energy nucleons (ii) $$ T\overline{T} $$ T T ¯ deformations of certain canonical scalar field theories with a potential. We find explicit soliton solutions of these models with sine-Gordon and Higgs-type potentials. We prove that the $$ T\overline{T} $$ T T ¯ deformation of a theory of a given potential does not correct the mass of the soliton of the undeformed one. We further conjecture the form of breather solutions of these models. We show that certain $$ T\overline{T} $$ T T ¯ deformed actions admit shockwave solutions that generalize those of Heisenberg’s Lagrangian.

Abstract licence: CC BY

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