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)L×SU(N)R×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)Vⁿ. 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.