Quasi-super-renormalizable models

We study softly broken supersymmetric N = 4 Yang-Mills theories. In the absence of finiteness constraints among the soft-breaking terms, we term these quasi-super-renormalizable. We show that all the constraints leading to finiteness constitute an infrared fixed hypersurface. We argue that an ultimate finite globally supersymmetric model requires fine-tuning; however, for the purpose of model building at some pseudo-infrared scale, finite theories may be useful. Thus, quasi-super-renormalizable N = 4 can have a nearly finite theory as its low-energy effective field theory. We conclude with some further observations on scale-invariant theories.