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

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.

arXiv comment23 pages, 5 figures; references added; plots and comments added

References in corpus (12)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• An integrable Lorentz-breaking deformation of two-dimensional CFTs
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• Modular invariance and uniqueness of $T\bar{T}$ deformed CFT
• $T\bar{T}$-deformations in closed form
• $T\bar{T}$ deformed partition functions
• Generalised Born-Infeld models, Lax operators and the $\text{T}\bar{\text{T}}$ perturbation
• More on Heisenberg's model for high energy nucleon-nucleon scattering
• Integrability and Renormalization under $T\bar{T}$
• A Non-Abelian Analogue of DBI from $T\overline{T}$

Cited by in corpus (3)

• Composite operators in $T\bar{T}$-deformed free QFTs
• $T\bar{T}$ deformations and the pp wave correspondence
• A $T\bar{T}$-like deformation of the Skyrme model and the Heisenberg model of nucleon-nucleon scattering