  We numerically evaluate the one-loop counterterms for the four-dimensional
Wess-Zumino model formulated on the lattice using Ginsparg-Wilson fermions of
the overlap (Neuberger) variety, together with an auxiliary fermion (plus
superpartners), such that a lattice version of $U(1)_R$ symmetry is exactly
preserved in the limit of vanishing bare mass. We confirm previous findings by
other authors that at one loop there is no renormalization of the
superpotential in the lattice theory, but that there is a mismatch in the
wavefunction renormalization of the auxiliary field. We study the range of the
Dirac operator that results when the auxiliary fermion is integrated out, and
show that localization does occur, but that it is less pronounced than the
exponential localization of the overlap operator. We also present preliminary
simulation results for this model, and outline a strategy for nonperturbative
improvement of the lattice supercurrent through measurements of supersymmetry
Ward identities. Related to this, some benchmarks for our graphics processing
unit code are provided. Our simulation results find a nearly vanishing vacuum
expectation value for the auxiliary field, consistent with approximate
supersymmetry at weak coupling.
