SU(2) Yang-Mills theory with extended supersymmetry in a background magnetic field

The vacuum structure of N = 2 (and N = 4) supersymmetric Yang-Mills theory is analyzed in detail by considering the effective potential for constant background scalar-magnetic fields within different approximations. We compare the one-loop approximation with or without instanton improved effective coupling with the one-loop result in the dual description. For N = 2 we find that non-perturbative monopole degrees of freedom remove the non-trivial minima present in the (improved) one-loop potential in the strong-coupling regime. The combination of Yang-Mills theory and the dual description leads to a self-consistent effective potential over the full range of background fields.