A lattice study of the two-dimensional Wess Zumino model

TL;DR

This study uses numerical simulations to explore non-perturbative effects in the two-dimensional Wess-Zumino model, revealing solitons and partial supersymmetry breaking that challenge previous perturbative assumptions.

Contribution

First non-perturbative lattice simulation demonstrating solitons and supersymmetry breaking effects in the 2D Wess-Zumino model.

Findings

Existence of solitons interpolating between vacua.

Partial supersymmetry breaking in soliton backgrounds.

Volume-dependent critical mass for phase transition.

Abstract

We present results from a numerical simulation of the two-dimensional Euclidean Wess-Zumino model. In the continuum the theory possesses N=1 supersymmetry. The lattice model we employ was analyzed by Golterman and Petcher in \cite{susy} where a perturbative proof was given that the continuum supersymmetric Ward identities are recovered without finite tuning in the limit of vanishing lattice spacing. Our simulations demonstrate the existence of important non-perturbative effects in finite volumes which modify these conclusions. It appears that in certain regions of parameter space the vacuum state can contain solitons corresponding to field configurations which interpolate between different classical vacua. In the background of these solitons supersymmetry is partially broken and a light fermion mode is observed. At fixed coupling the critical mass separating phases of broken and unbroken supersymmetry appears to be volume dependent. We discuss the implications of our results for continuum supersymmetry breaking.