Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

TL;DR

This paper investigates supercurrent conservation in the lattice Wess-Zumino model using Ginsparg-Wilson fermions, demonstrating one-loop conservation and nonperturbative supercurrent nonconservation with Wilson fermions.

Contribution

It shows that the almost naive supercurrent is conserved at one loop with Ginsparg-Wilson fermions, unlike Wilson fermions, and provides nonperturbative evidence of supercurrent nonconservation.

Findings

Supercurrent conserved at one loop with Ginsparg-Wilson fermions.

Supercurrent not conserved with Wilson fermions.

Nonperturbative evidence of supercurrent nonconservation in Monte Carlo simulations.

Abstract

We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses 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 show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.