Non-Abelian monopole-vortex complex

TL;DR

This paper constructs monopole-vortex complex solutions in softly broken N=2 SQCD with hierarchical symmetry breaking, revealing exact zero modes and a dual non-Abelian gauge symmetry, advancing understanding of non-Abelian monopoles.

Contribution

It introduces explicit monopole-vortex solutions with exact orientational zero modes in a hierarchical symmetry breaking framework, clarifying the role of dual non-Abelian gauge symmetry.

Findings

Existence of exact CP(N-1) zero modes on monopole-vortex complexes.

Monopoles and vortices transform under a new unbroken SU(N) symmetry.

Clarification of the origin of dual non-Abelian gauge symmetry.

Abstract

In the context of softly broken N=2 supersymmetric quantum chromodynamics (SQCD), with a hierarchical gauge symmetry breaking SU(N+1) -> U(N) -> 1, at scales v1 and v2, respectively, where v1 >> v2, we construct monopole-vortex complex soliton-like solutions and examine their properties. They represent the minimum of the static energy under the constraint that the monopole and antimonopole positions sitting at the extremes of the vortex are kept fixed. They interpolate the 't Hooft-Polyakov-like regular monopole solution near the monopole centers and a vortex solution far from them and in between. The main result, obtained in the theory with Nf=N equal-mass flavors, is concerned with the existence of exact orientational CP(N-1) zero modes, arising from the exact color-flavor diagonal SU(N)_{C+F} global symmetry. The "unbroken" subgroup SU(N) \subset SU(N+1) with which the na\"ive notion of non-Abelian monopoles and the related difficulties were associated, is explicitly broken at low energies. The monopole transforms nevertheless according to the fundamental representation of a new exact, unbroken SU(N) symmetry group, as does the vortex attached to it. We argue that this explains the origin of the dual non-Abelian gauge symmetry.