Domain Walls with Non-Abelian Clouds

TL;DR

This paper studies non-Abelian domain walls in gauge theories, revealing their internal non-Abelian NG modes, constructing their effective theories, and exploring their interactions, bound states, and symmetry breaking effects.

Contribution

It introduces the concept of non-Abelian clouds on domain walls, constructs the moduli space metric, and analyzes the dynamics and symmetry breaking of these walls in specific gauge theories.

Findings

Non-Abelian clouds spread between domain walls and induce long-range repulsive forces.

Constructed the moduli space metric and Kahler potential for effective theories on the walls.

Identified symmetry breaking patterns and NG modes localized on the walls.

Abstract

Domain walls in U(N) gauge theories, coupled to Higgs scalar fields with degenerate masses, are shown to possess normalizable non-Abelian Nambu-Goldstone(NG) modes, which we call non-Abelian clouds. We construct the moduli space metric and its Kahler potential of the effective field theory on the domain walls, by focusing on two models: a U(1) gauge theory with several charged Higgs fields, and a U(N) gauge theory with 2N Higgs fields in the fundamental representation. We find that non-Abelian clouds spread between two domain walls and that their rotation induces long-range repulsive force, in contrast to a U(1) mode in models with fully non-degenerate masses which gives short-range force. We also construct a bound state of dyonic domain walls by introducing the imaginary part of the Higgs masses. In the latter model we find that when all walls coincide SU(N)_L x SU(N)_R x U(1) symmetry is broken down to SU(N)_V, and U(N)_A NG modes and the same number of quasi-NG modes are localized on the wall. When n walls separate, off diagonal elements of U(n) NG modes have wave functions spreading between two separated walls (non-Abelian clouds), whereas some quasi-NG modes turn to NG bosons as a result of further symmetry breaking U(n)_V --> U(1)_V^n. In the case of 4+1 dimensional bulk, we can dualize the effective theory to the supersymmetric Freedman-Townsend model of non-Abelian 2-form fields.