Non-Abelian monopoles and the vortices that confine them

Non-Abelian magnetic monopoles of Goddard-Nuyts-Olive-Weinberg type have recently been shown to appear as the dominant infrared degrees of freedom in a class of softly broken N = 2 supersymmetric gauge theories in which the gauge group G is broken to various non-Abelian subgroups H by an adjoint Higgs VEV When the low-energy gauge group H is further broken completely by, e.g., squark VEVs, the monopoles representing pi(2)(GIH) are confined by the non-Abelian vortices arising from the breaking of H, discussed recently [hep-th/0307278]. By considering the system with G = SU(N + 1), H =S(U) X U (1)/Z(N), as an example, we show that the total magnetic flux of the minimal monopole agrees precisely with the total magnetic flux flowing along the single minimal vortex. The possibility for such an analysis reflects the presence of free parameters in the theory-the bare quark mass in and the adjoint mass it-such that for m much greater than mu the topologically nontrivial solutions of vortices and of unconfined monopoles exist at distinct energy scales. (C) 2004 Elsevier B.V All rights reserved.