We investigate the short distance fate of distinct classes of not
asymptotically free supersymmetric gauge theories. Examples include super QCD
with two adjoint fields and generalised superpotentials, gauge theories without
superpotentials and with two types of matter representation and semi-simple
gauge theories such as quivers. We show that for the aforementioned theories
asymptotic safety is nonperturbatively compatible with all known constraints.Comment: LaTeX 14 pages, several figures, added another exampl
