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 $\theta$ 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 $\theta_{ph}$; as it is varied there is however a phase transition at $\theta_{ph} =-\pi, \pi, 3\pi, \ldots$. At these values of $\theta_{ph}$ the vacuum is doubly degenerate and CP invariance is spontaneously broken \`a la Dashen. Due to the instanton-induced renormalization effect the low energy effective $\theta$ parameter remains small irrespectively of $\theta_{ph}$ as long as the gaugino mass is sufficiently small.