Small deformations of kinks and walls

TL;DR

This paper develops a perturbation scheme to analyze how weak self-interactions modify scalar field kinks and walls, revealing effects like asymmetric potentials and vacuum bubble formation.

Contribution

It introduces a Rayleigh-Schrodinger type perturbation method for scalar defects and demonstrates its application to cubic perturbations of quartic kinks.

Findings

Perturbations cause asymmetry in scalar potentials.

Vacuum bubbles can form due to nondegenerate vacua.

First-order corrections modify defect solutions.

Abstract

A Rayleigh-Schrodinger type of perturbation scheme is employed to study weak self-interacting scalar potential perturbations occurring in scalar field models describing 1D domain kinks and 3D domain walls. The solutions for the unperturbed defects are modified by the perturbing potentials. An illustration is provided by adding a cubic potential to the familiar quartic kink potential and solving for the first order correction to the kink solution, using a "slab approximation". A result is the appearance of an asymmetric scalar potential with different, nondegenerate, vacuum values and the subsequent formation of vacuum bubbles.