Domain wall solutions with Abelian gauge fields

TL;DR

This paper investigates kink solutions in a model with two complex scalars and two Abelian gauge fields, revealing domain walls that separate regions with different magnetic field configurations.

Contribution

It introduces a novel model with coupled scalar and gauge fields exhibiting unique domain wall solutions with magnetic field variations.

Findings

Domain walls preserve U(1) symmetries in vacua

Magnetic fields are constant within domains

Domain walls connect regions with different magnetic properties

Abstract

We study kink (domain wall) solutions in a model consisting of two complex scalar fields coupled to two independent Abelian gauge fields in a Lagrangian that has $U(1)\times U(1)$ gauge plus $\mathbb{Z}_2$ discrete symmetry. We find consistent solutions such that while the U(1) symmetries of the fields are preserved while in their respective vacua, they are broken on the domain wall. The gauge field solutions show that the domain wall is sandwiched between domains with constant magnetic fields.