Domain wall solutions with Abelian gauge fields

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.

Comments: 11 pages, 6 figures, JHEP for style, but to appear in PLB. Added discussion about the boundary conditions and the physical picture based on superconductivity. Reference added