Exact lattice Ward-Takahashi identity for the N=1 Wess-Zumino model

TL;DR

This paper demonstrates that a lattice formulation of the N=1 Wess-Zumino model with Ginsparg-Wilson relation preserves the Ward-Takahashi identity and supersymmetry in the continuum limit through perturbative analysis.

Contribution

It establishes an exact lattice Ward-Takahashi identity for the N=1 Wess-Zumino model and shows how it ensures supersymmetry restoration in the continuum limit.

Findings

Ward-Takahashi identity holds at finite lattice spacing and in continuum limit

Wave functions for scalar and fermion fields coincide in the continuum limit

Supersymmetry is restored automatically in the continuum limit

Abstract

We consider a lattice formulation of the four dimensional N=1 Wess-Zumino model that uses the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. We show that the corresponding Ward-Takahashi identity is satisfied, both at fixed lattice spacing and in the continuum limit. The calculation is performed in lattice perturbation theory up to order $g^2$ in the coupling constant. We also show that this Ward-Takahashi identity determines the finite part of the scalar and fermion renormalization wave functions which automatically leads to restoration of supersymmetry in the continuum limit. In particular, these wave functions coincide in this limit.