Non-Abelian monopole-vortex complex

In the context of softly broken N=2 supersymmetric quantum chromodynamics, with a hierarchical gauge symmetry breaking SU(N+1)→v1U(N)→v21, v1>>v2, we construct monopole-vortex complex solitonlike 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 CPN-1 zero modes, arising from the exact color-flavor diagonal SU(N)C+F global symmetry. The ''unbroken'' subgroup SU(N) subset of SU(N+1), with which the naive 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.