Stability of Kink Defects in a Deformed O(3) Linear Sigma Model

TL;DR

This paper investigates the stability and structure of kink solutions in a generalized O(3) linear Sigma model, revealing a moduli space of solutions and analyzing their stability using Morse Theory.

Contribution

It introduces a set of first-order equations for kinks in a deformed O(3) model and characterizes the moduli space and stability properties of these solutions.

Findings

Kinks form a moduli space with a natural compactification.

Generic kinks are unstable according to Morse Theory.

Energy sum rules help classify kink solutions.

Abstract

We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account certain kink energy sum rules we show that the variety of kinks has the structure of a moduli space that can be compactified in a fairly natural way. The generic kinks, however, are unstable and Morse Theory provides the framework for the analysis of kink stability.