Scalar triplet on a domain wall: an exact solution

TL;DR

This paper presents an exact analytic solution for a domain wall in a scalar field model with a triplet, revealing localized degrees of freedom and analyzing stability depending on model parameters.

Contribution

The paper provides the first exact solution describing a domain wall with a localized triplet field and explores its stability and degrees of freedom.

Findings

Exact analytic solution for the domain wall with triplet field

Localized degrees of freedom depend on model parameters

Stability analysis of the domain wall with and without the triplet field

Abstract

We study a model with a real scalar Higgs field and a scalar triplet field that allows existence of a topological defect -- a domain wall. The wall breaks the global $O(3)$ symmetry of the model, which gives rise to non-Abelian orientational degrees of freedom. We found an exact analytic solution that describes a domain wall with a localized configuration of the triplet field on it. This solution enables one to calculate contributions to the action from the orientational and translational degrees of freedom of the triplet field. We also study the linear stability of the domain wall with the triplet field switched off. We obtain that degrees of freedom localized on the wall can appear or do not appear depending on the parameters of the model.