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

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 nonlinear 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 g3 (two loops), and the Ward-Takahashi identity (containing 110 connected nontadpole Feynman diagrams) is satisfied at fixed lattice spacing thanks to this exact lattice supersymmetry. © 2013 American Physical Society.