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

TL;DR

This paper demonstrates that the lattice N=1 Wess-Zumino model, formulated with Ginsparg-Wilson fermions, inherently restores continuum supersymmetry at order g^2 without fine tuning, ensuring scalar and fermion wave function equality.

Contribution

It provides an explicit proof that lattice supersymmetry leads to continuum supersymmetry restoration without fine tuning, using Ward-Takahashi identities up to order g^2.

Findings

Supersymmetry is restored at order g^2 on the lattice.

Scalar and fermion wave functions coincide in the continuum limit.

The lattice formulation respects a generalized supersymmetry without fine tuning.

Abstract

The lattice Wess-Zumino model written in terms of the Ginsparg-Wilson relation is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. By studying the associated Ward-Takahashi identity up to order $g^2$ we show that this lattice supersymmetry automatically leads to restoration of continuum supersymmetry without fine tuning. In particular, the scalar and fermion renormalization wave functions coincide.