Transitions between topologically non-trivial configurations

TL;DR

This paper investigates the formation and evolution of topologically non-trivial soliton configurations in a two-scalar field model, providing insights into their classification, dynamics, and resulting domain wall structures.

Contribution

It introduces a simple expression for the winding number in a two-field model and analyzes how evolution scenarios alter topological classes.

Findings

Derived a formula for the winding number of field configurations.

Identified scenarios that change the topological class during evolution.

Linked topological configurations to domain wall formation in 3D space.

Abstract

We study formation and evolution of solitons within a model with two real scalar fields with the potential having a saddle point. The set of these configurations can be split into disjoint equivalence classes. We give a simple expression for the winding number of an arbitrary closed loop in the field space and discuss the evolution scenarios that change the winding number. These non-trivial field configurations lead to formation of the domain walls in the three-dimensional physical space.