Thick domain walls in a polynomial approximation

TL;DR

This paper models relativistic domain walls using a polynomial approximation, deriving equations for their core evolution and width, and analyzing effects of curvature and specific geometries like toroidal walls.

Contribution

It introduces a polynomial approximation framework to study domain wall dynamics, including core evolution and width changes, with perturbative solutions for nonlinear equations.

Findings

Core obeys Nambu-Goto equation for a relativistic membrane.

Width of the domain wall increases with curvature.

Toroidal domain wall evolution analyzed.

Abstract

Relativistic domain walls are studied in the framework of a polynomial approximation to the field interpolating between different vacua and forming the domain wall. In this approach we can calculate evolution of a core and of a width of the domain wall. In the single, cubic polynomial approximation used in this paper, the core obeys Nambu-Goto equation for a relativistic membrane. The width of the domain wall obeys a nonlinear equation which is solved perturbatively. There are two types of corrections to the constant zeroth order width: the ones oscillating in time, and the corrections directly related to curvature of the core. We find that curving a static domain wall is associated with an increase of its width. As an example, evolution of a toroidal domain wall is investigated.