Soliton, breather and shockwave solutions of the Heisenberg and the TT¯ deformations of scalar field theories in 1+1 dimensions - Nastase, Horatiu [UNESP]; Sonnenschein, Jacob (Springer Nature, 2021)
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) TT¯ 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 TT¯ 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 TT¯ deformed actions admit shockwave solutions that generalize those of Heisenberg’s Lagrangian.
Keywords: Field Theories in Lower Dimensions; Solitons Monopoles and Instantons