Lattice Wess-Zumino model with Ginsparg-Wilson fermions: One-loop results and GPU benchmarks

Abstract

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.