N=2 Wess-Zumino model on the d=2 Euclidean lattice

TL;DR

This paper investigates the N=2 Wess-Zumino model on a 2D Euclidean lattice, comparing Wilson and Ginsparg-Wilson fermions, and examines supersymmetry restoration and divergences as the lattice spacing approaches zero.

Contribution

It provides a detailed analysis of supersymmetry restoration, divergence behavior, and the effects of extra couplings in lattice formulations of the N=2 Wess-Zumino model.

Findings

Wilson fermions induce linear divergences in tadpole diagrams.

Ginsparg-Wilson fermions avoid these divergences.

Supersymmetry in correlation functions is recovered as lattice spacing approaches zero.

Abstract

We examine the N=2 Wess-Zumino model defined on the $d=2$ Euclidean lattice in connection with a restoration of the Leibniz rule in the limit $a\to0$ in perturbatively finite theory. We are interested in the difference between the Wilson and Ginsparg-Wilson fermions and in the effects of extra interactions introduced by an analysis of Nicolai mapping. As for the Wilson fermion, it induces a linear divergence to individual tadpole diagrams in the limit $a\to0$, which is absent in the Ginsparg-Wilson fermion. This divergence suggests that a careful choice of lattice regularization is required in a reliable numerical simulation. As for the effects of the extra couplings introduced by an analysis of Nicolai mapping, the extra couplings do not completely remedy the supersymmetry breaking in correlation functions induced by the failure of the Leibniz rule in perturbation theory, though those couplings ensure the vanishing of vacuum energy arising from disconnected diagrams. Supersymmetry in correlation functions is recovered in the limit $a\to 0$ {\em with or without} those extra couplings. In the context of lattice theory, it may be properly said that supersymmetry does not improve ultraviolet properties but rather it is well accommodated in theories with good ultraviolet properties.