Constraints on ultraviolet-stable fixed points in supersymmetric gauge theories - art. no. 036010

We consider the possibility that some supersymmetric gauge theories which a re not asymptotically free can be governed by ultraviolet-stable fixed poin ts. If this scenario can be realized, gaugino masses will exhibit power-law running with scale, providing a possible solution to the supersymmetric fl avor problem. While naive perturbative calculations hint at the appearance of ultraviolet-stable fixed points in certain theories, there are strong co nstraints following from limits on the scaling dimensions of gauge-invarian t operators, positivity of central charges, and Cardy's conjectured constra int on the flow of the Euler coefficient in the stress tensor trace anomaly . Also, we prove that if ultraviolet-stable fixed points do exist, they can not occur in the perturbative regime of a renormalizable model, and that al l-orders results in the limit of large numbers of chiral superfields are ne cessarily inconclusive. However, we argue that the general idea of ultravio let-stable fixed points in supersymmetric gauge theories is viable, and we exhibit models that can satisfy all known constraints.