  We study the low-energy dynamics of all N=1 supersymmetric gauge theories
whose basic gauge invariant fields are unconstrained. This set includes all
theories whose matter Dynkin index is less than the index of the adjoint
representation. We study the dynamically generated superpotential in these
theories, and show that there is a W=0 branch if and only if anomaly matching
is satisfied at the origin. An interesting example studied in detail is SO(13)
with a spinor, a theory with a dynamically generated W and no anomaly matching
at the origin. It flows via the Higgs mechanism to SU(6) with a three-index
antisymmetric tensor, a theory with a W=0 branch and anomaly matching at the
origin.
