  All supersymmetric gauge theories based on simple groups which have an affine
quantum moduli space, i.e. one generated by gauge invariants with no relations,
W=0, and anomaly matching at the origin, are classified. It is shown that the
only theories with no gauge invariants (and moduli space equal to a single
point) are the two known examples, SU(5) with 5-bar + 10 and SO(10) with a
spinor. The index of the matter representation must be at least as big as the
index of the adjoint in theories which have a non-trivial relation among the
gauge invariants.
