### Abstract

It is argued that the dual transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G → H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The transformation law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v_{1} ≫ v_{2}) G over(→, v_{1}) H over(→, v_{2}) 1, under an unbroken, exact color-flavor diagonal symmetry H_{C + F} ∼ over(H, ̃). The transformation property among the regular monopoles characterized by π_{2} (G / H), follows from that among the non-Abelian vortices with flux quantized according to π_{1} (H), via the isomorphism π_{1} (G) ∼ π_{1} (H) / π_{2} (G / H). Our idea is tested against the concrete models-softly-broken N = 2 supersymmetric SU (N), SO (N) and USp (2 N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v_{1} ≫ v_{2} ≫ Λ) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v_{1}, v_{2} ∼ Λ).

Original language | English |
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Pages (from-to) | 161-187 |

Number of pages | 27 |

Journal | Nuclear Physics B |

Volume | 780 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Oct 1 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics B*,

*780*(3), 161-187. https://doi.org/10.1016/j.nuclphysb.2007.03.040