Non-Abelian duality from vortex moduli: A dual model of color-confinement

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, v1≫v2) G→v1H→v21, under an unbroken, exact color-flavor diagonal symmetry HC+F∼H˜. The transformation property among the regular monopoles characterized by π2(G/H), follows from that among the non-Abelian vortices with flux quantized according to π1(H), via the isomorphism π1(G)∼π1(H)/π2(G/H). Our idea is tested against the concrete models-softly-broken N=2 supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v1≫v2≫Λ) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v1,v2∼Λ).