Domain Walls with Non-Abelian Clouds

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.