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arXiv · 2010.12413

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

Horatiu Nastase·Jacob Sonnenschein
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Abstract

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) $T\bar T$ 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 $T\bar T$ 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 $T\bar T$ deformed actions admit shockwave solutions that generalize those of Heisenberg's Lagrangian.

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Horatiu Nastase, Jacob Sonnenschein. 2020-10-23. Soliton, breather and shockwave solutions of the Heisenberg and the $T\bar T$ deformations of scalar field theories in 1+1 dimensions. https://doi.org/10.1007/jhep04(2021)106

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