Duality, Superconvergence and the Phases of Gauge Theories

Results about the phase structure of certain N=1 supersymmetric gauge theories, which have been obtained as a consequence of holomorphy and `electric-magnetic' duality, are shown to be in quantitative agreement with corresponding consequences of analyticity and superconvergence of the gauge field propagator. This connection is of interest, because the superconvergence arguments for confinement are not restricted to theories with supersymmetry. The method of reduction in the space of coupling parameters is used in order to define, beyond the matching conditions, an asymptotically free, dual magnetic theory involving Yukawa couplings.