  Arguments for the confinement of transverse gauge field excitations, which
are based upon superconvergence relations of the propagator, and upon the BRST
algebra, are reviewed and applied to supersymmetric models. They are shown to
be in agreement with recent results obtained as a consequence of holomorphy and
duality in certain $N=1$ SUSY models. The significance of the one loop
anomalous dimension of the gauge field in the Landau gauge is emphasized. For
the models considered, it is shown to be proportional, with negative relative
sign, to the one loop coefficient of the renormalization group function for the
{\it dual map} of the original theory.
