SUPERSYMMETRIC GAUGE THEORIES WITH AN AFFINE QUANTUM MODULI SPACE
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 (i.e., moduli space equal to a single point) are the two known examples, SU(5) with {ovr 5}+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 nontrivial relation among the gauge invariants. {copyright} {ital 1998} {ital The American Physical Society}