  We generalize the Gervais-Neveu gauge to four-dimensional N=1 superspace. The
model describes an N=2 super Yang-Mills theory. All chiral superfields (N=2
matter and ghost multiplets) exactly cancel to all loops. The remaining
hermitian scalar superfield (matrix) has a renormalizable massive propagator
and simplified vertices. These properties are associated with N=1 supergraphs
describing a superstring theory on a random lattice world-sheet. We also
consider all possible finite matrix models, and find they have a universal
large-color limit. These could describe gravitational strings if the
matrix-model coupling is fixed to unity, for exact electric-magnetic
self-duality.
