  Recently (hep-th/0104171) we considered N=2 super Yang-Mills with a N=2 mass
breakingn term and showed the existence of BPS Z_{k}-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 Z_{k}-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.
