From the Dirac Operator to Wess-Zumino Models on Spatial Lattices

TL;DR

This paper explores lattice formulations of two-dimensional Wess-Zumino models, demonstrating how different lattice derivatives affect chiral fermions and supersymmetry, and analyzing zero modes across coupling regimes.

Contribution

It introduces the use of the antisymmetric SLAC derivative to preserve chiral fermions and minimize lattice artifacts in supersymmetric models.

Findings

Non-antisymmetric derivatives break supersymmetry and exclude chiral fermions.

The SLAC derivative allows chiral fermions with minimal artifacts.

Complete zero mode analysis for arbitrary coupling regimes.

Abstract

We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the nonlocal and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess-Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.