Zₖ String fluxes and monopole confinement in non-Abelian theories

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Recently (hep-th/0104171) we considered N=2 super Yang-Mills with a N=2 mass breakingn term and showed the existence of BPS Zₖ-string solutions for arbitrary simple gauge groups which are spontaneously broken to non-Abelian residual gauge groups. We also calculated their string tensions exactly. In doing so, we have considered in particular the hypermultiplet in the same representation as the one of a diquark condensate. In the present work we analyze some of the different phases of the theory and find that the magnetic fluxes of the monopoles are multiple of the fundamental Zₖ-string flux, allowing for monopole confinement in one of the phase transitions of the theory. We also calculate the threshold length for a string breaking. Some of these confining theories can be obtained by adding a N=0 deformation term to N=2 or N=4 superconformal theories.