Domain Wall Solitons Arising in Classical Gauge Field Theories

TL;DR

This paper explores the existence and explicit construction of domain wall solitons in classical gauge field theories, revealing new integrability results in Abelian models and existence theorems in non-Abelian theories.

Contribution

It provides explicit solutions in Abelian gauge theories and establishes existence theorems for non-Abelian domain wall solutions using variational methods.

Findings

Explicit solutions for Abelian gauge domain walls.

Existence theorems for non-Abelian gauge domain walls.

Enhanced understanding of integrability in Liouville equations.

Abstract

Domain wall solitons are basic constructs realizing phase transitions in various field-theoretical models and are solutions to some nonlinear ordinary differential equations descending from the corresponding full sets of governing equations in higher dimensions. In this paper, we present a series of domain wall solitons arising in several classical gauge field theory models. In the context of the Abelian gauge field theory, we unveil the surprising result that the solutions may explicitly be constructed, which enriches our knowledge on integrability of the planar Liouville type equations in their one-dimensional limits. In the context of the non-Abelian gauge field theory, we obtain some existence theorems for domain wall solutions arising in the electroweak type theories by developing some methods of calculus of variations formulated as direct and constrained minimization problems over a weighted Sobolev space.