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 K\"ahler 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 a long-range repulsive force, in contrast to a U (1) mode in models with fully nondegenerate masses which gives a 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) ₋ (N) ₑ (1) symmetry is broken down to SU (N) ₕ, and U (N) ₀ 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) ₕ (1) ₕ^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.