Domain wall networks on solitons

TL;DR

This paper investigates the formation and structure of domain wall networks on solitons in a (3+1)-dimensional scalar field theory with U(1) x Z_n symmetry, revealing how specific polyhedral networks can form on Q-balls.

Contribution

It introduces a numerical study of domain wall networks on solitons, specifically on Q-balls, and explains the geometric restrictions on possible network configurations.

Findings

Domain wall networks can form on the surface of Q-balls.

Networks can resemble edges of spherical polyhedra with junctions.

Only certain polyhedral configurations are possible due to symmetry constraints.

Abstract

Domain wall networks on the surface of a soliton are studied in a simple theory. It consists of two complex scalar fields, in (3+1)-dimensions, with a global U(1) x Z_n symmetry, where n>2. Solutions are computed numerically in which one of the fields forms a Q-ball and the other field forms a network of domain walls localized on the surface of the Q-ball. Examples are presented in which the domain walls lie along the edges of a spherical polyhedron, forming junctions at its vertices. It is explained why only a small restricted class of polyhedra can arise as domain wall networks.