On expansion in the width for domain walls

TL;DR

This paper reexamines the expansion method in the width for domain wall solutions, revealing singular perturbation issues and deriving second-order solutions without effective actions, showing differences in dynamics between cylindrical and spherical walls.

Contribution

It introduces a consistent perturbative expansion for domain walls using the Hilbert-Chapman-Enskog method, avoiding effective actions and highlighting differences in wall rigidity.

Findings

Zeros of the scalar field do not follow Nambu-Goto trajectories.

Spherical domain walls exhibit effective rigidity.

Second-order solutions are obtained without effective actions.

Abstract

The well-known idea to construct domain wall type solutions of field equations by means of an expansion in the width of the domain wall is reexamined. We observe that the problem involves singular perturbations. Hilbert-Chapman-Enskog method is used to construct a consistent perturbative expansion. We obtain the solutions to the second order in the width without introducing an effective action for the domain wall. We find that zeros of the scalar field in general do not lie on a Nambu-Goto trajectory. As examples we consider cylindrical and spherical domain walls. We find that the spherical domain wall, in contradistinction to the cylindrical one, shows an effective rigidity.