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

TL;DR

This paper evaluates one-loop counterterms for a lattice Wess-Zumino model with Ginsparg-Wilson fermions, confirming no superpotential renormalization, studying localization properties, and providing GPU benchmarks and preliminary simulation results.

Contribution

It presents the first one-loop analysis of the lattice Wess-Zumino model with Ginsparg-Wilson fermions, including localization and simulation benchmarks.

Findings

No renormalization of the superpotential at one loop

Wavefunction renormalization mismatch for auxiliary fields

GPU code benchmarks and preliminary simulation results

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.