Abstract
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.
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