Lattice Wess-Zumino Model Simulation with GPUs

Abstract

We have numerically evaluated 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 have conrmed previous ndings 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 eld. We studied the range of the Dirac operator that results when the auxiliary fermion is integrated out, and showed that localization does occur, but that it is less pronounced than the exponential localization of the overlap operator. We also presented 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 were provided. Our simulation results found a nearly vanishing vacuum expectation value for the auxiliary eld, consistent with approximate supersymmetry at weak coupling.