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

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.