### 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 Kähler 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.

Original language | English |
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Article number | 125008 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 77 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2008 Jun 5 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*77*(12), [125008]. https://doi.org/10.1103/PhysRevD.77.125008