Asymptotic freedom, infrared convergence and supersymmetry

The conditions for infrared convergence and asymptotic freedom are investigated for a system in which (in order to produce a spontaneous breakdown) a supersymmetric matter-matter interaction is added to the supersymmetric Yang-Mills Lagrangian. It is found that, in contrast to conventional theory, the conditions imposed by the asymptotic freedom of the matter-matter interaction are not stringent, and are automatically satisfied for adjoint representation. The conditions for infrared convergence are also not too stringent. However the joint conditions for asymptotic freedom and infrared convergence turn out to be quite stringent. Nevertheless, a model is proposed which, subject to some reservations, appears to satisfy the joint conditions. (Auth.)