Nonabelian Monopoles and the Vortices that Confine Them

Nonabelian 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 ${\cal N}=2$ supersymmetric gauge theories in which the gauge group $G$ is broken to various nonabelian 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 $\pi_2(G/H)$ are confined by the nonabelian vortices arising from the breaking of $H$, discussed recently (hep-th/0307278). By considering the system with $G=SU(N+1)$, $ H = {SU(N) \times U(1) {\o}{\mathbb 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 $m$ and the adjoint mass $\mu$ - such that for $m \gg \mu$ the topologically nontrivial solutions of vortices and of unconfined monopoles exist at distinct energy scales.