Two-loop Wess-Zumino model with exact supersymmetry on the lattice

TL;DR

This paper presents a lattice formulation of the four-dimensional N=1 Wess-Zumino model that maintains exact supersymmetry at finite lattice spacing, verified through two-loop perturbative calculations and Ward-Takahashi identities.

Contribution

It introduces a lattice action with exact supersymmetry using the Ginsparg-Wilson relation and demonstrates its validity through perturbative checks up to two loops.

Findings

Exact supersymmetry is preserved at finite lattice spacing.

Ward-Takahashi identities are satisfied at two-loop order.

The formulation is consistent with perturbative calculations.

Abstract

We consider a lattice formulation of the four dimensional N=1 Wess-Zumino model in terms of the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. The lattice action is invariant under a deformed supersymmetric transformation which is non-linear in the scalar fields and it is determined by an iterative procedure in the coupling constant to all orders in perturbation theory. We also show that the corresponding Ward-Takahashi identity is satisfied at fixed lattice spacing. The calculation is performed in lattice perturbation theory up to order $g^3$ (two-loop) and the Ward-Takahashi identity (containing 110 connected non-tadpole Feynman diagrams) is satisfied at fixed lattice spacing thanks to this exact lattice supersymmetry.