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

TL;DR

This paper explores a duality between non-Abelian monopoles and vortices in gauge theories, providing a framework that connects classical configurations with quantum low-energy effective actions, enhancing understanding of color confinement.

Contribution

It introduces a dual transformation law linking monopoles and vortices in non-Abelian gauge theories, validated through concrete supersymmetric models.

Findings

Consistent duality relations in supersymmetric models

Monopole-vortex correspondence established via homotopy groups

Framework applicable to understanding color confinement

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 -> H -> 0, under an unbroken, exact color-flavor diagonal symmetry H_{C+F} \sim {\tilde H}. The transformation property among the regular monopoles characterized by \pi_2(G/H), follows from that among the non-Abelian vortices with flux quantized according to \pi_1(H), via the isomorphism \pi_1(G) \sim \pi_1(H) / \pi_2(G/H). Our idea is tested against the concrete models -- softly-broken {\cal N}=2 supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v_1 >> v_2 >> \Lambda) 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 \sim \Lambda).