Stability Equation and Two-Component Eigenmode for Domain Walls in a Scalar Potential Model

TL;DR

This paper explores the stability of domain walls in a scalar potential model using supersymmetric quantum mechanics, deriving a matrix superpotential and analyzing stability of BPS and non-BPS states.

Contribution

It introduces a matrix superpotential framework to analyze stability of domain walls, connecting supersymmetric quantum mechanics with classical configurations.

Findings

BPS states are stable due to the matrix superpotential analysis.

Non-BPS states are shown to be unstable via fluctuation Hessian.

The approach links supersymmetry algebra with classical stability analysis.

Abstract

The connection between the supersymmetric quantum mechanics involving two-component eigenfunctions and the stability equation associated with two classical configurations is investigated, and a matrix superpotential is deduced. The issue of stability is ensured for the Bogomol'nyi-Prasad-Sommerfield (BPS) states on two domain walls in a scalar potential model containing up to fourth-order powers in the fields, which is explicit demonstrated using the intertwining operators in terms of 2x2-matrix superpotential in the algebraic framework of supersymmetry in quantum mechanics. Also, a non-BPS state is found to be non-stable via fluctuation hessian matrix.