  Superconvergence relations for the transverse gauge field propagator can be
used in order to show that the corresponding gauge quanta are not elements of
the physical state space, as defined by the BRST algebra. With a given gauge
group, these relations are valid for a limited region in the number of matter
fields, indicating a phase transition at the boundary. In the case of SUSY
gauge theories with matter fields in the fundamental representation, the
results predicted by superconvergence can be compared directly with those
obtained on the basis of duality and the conformal algebra. There is exact
agreement.
