Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model

TL;DR

This paper develops a lattice formulation of the two-dimensional N=2 Wess-Zumino model that preserves exact supersymmetry at finite lattice spacing and verifies its properties through numerical simulations.

Contribution

It introduces a lattice prescription that exactly preserves one supersymmetry and constructs additional approximate symmetries, enabling nonperturbative studies of supersymmetric models.

Findings

Exact supersymmetry is preserved at finite lattice spacing.

Mass gaps in boson and fermion sectors agree at weak coupling.

Lattice Ward identities are satisfied, confirming symmetry properties.

Abstract

We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving {\it exactly} a single supersymmetric invariance at finite lattice spacing $a$. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to $O(ga^2)$ where $g$ is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the massgaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.