Symmetries within domain walls

TL;DR

This paper examines the symmetry properties of domain walls in an SU(N)×Z_2 model, highlighting conditions under which the interior of the wall has less or more symmetry than the surrounding vacuum, relevant for brane and monopole interactions.

Contribution

It analyzes symmetry differences across domain walls in a specific gauge theory, providing insights into their structural and interaction properties.

Findings

Interior symmetry can be less than vacuum symmetry easily.

Achieving greater interior symmetry than the vacuum requires complex potential engineering.

Discusses implications for brane and monopole interactions.

Abstract

The comparison of symmetries in the interior and the exterior of a domain wall is relevant when discussing the correspondence between domain walls and branes, and also when studying the interaction of walls and magnetic monopoles. I discuss the symmetries in the context of an SU(N) times Z_2 model (for odd N) with a single adjoint scalar field. Situations in which the wall interior has less symmetry than the vacuum are easy to construct while the reverse situation requires significant engineering of the scalar potential.