Confinement, Supersymmetry Breaking and Theta Parameter Dependence in the Seiberg-Witten Model

Abstract

By using the standard perturbation theory we study the mass as well as $θ$ parameter dependence of the Seiberg-Witten theory with $SU(2)$ gauge group, supplemented with a $N=1$ supersymmetric as well as a smaller nonsupersymmetric (e.g.) gaugino mass. Confinement persists at all values of the bare vacuum parameter $θ_{ph}$; as it is varied there is however a phase transition at $θ_{ph} =-π, π, 3π, \ldots$. At these values of $θ_{ph}$ the vacuum is doubly degenerate and CP invariance is spontaneously broken à la Dashen. Due to the instanton-induced renormalization effect the low energy effective $θ$ parameter remains small irrespectively of $θ_{ph}$ as long as the gaugino mass is sufficiently small.