SUSY QM from Three Domain Walls in a Scalar Potential

TL;DR

This paper analyzes the classical stability of three-domain wall solutions in a scalar field system, linking supersymmetric quantum mechanics to stability equations, and providing insights into their stability properties.

Contribution

It introduces a novel connection between supersymmetric quantum mechanics and the stability analysis of three-domain wall solutions in scalar field theories.

Findings

Established the stability conditions for three-domain wall configurations.

Linked superpotential evaluations to stability equations.

Provided a framework for analyzing multi-field domain walls.

Abstract

We investigate the linear classical stability of Bogomol'nyi-Prasad-Sommerfield (BPS) on three domain wall solutions in a system of three coupled real scalar fields, for a general positive potential with a square form. From a field theoretic superpotential evaluated on the domain states, the connection between the supersymmetric quantum mechanics involving three-component eigenfunctions and the stability equation associated with three classical configurations is elaborated.