Low-dimensional Supersymmetric Lattice Models

TL;DR

This paper investigates supersymmetric lattice models in one and two dimensions, demonstrating improved simulation results and faster convergence to continuum values using specific derivatives and discretization techniques.

Contribution

It introduces improved lattice discretizations for supersymmetric models that enhance accuracy and convergence, including novel Wilson terms and the use of the SLAC derivative.

Findings

Wilson derivative with Stratonovitch discretization yields better finite lattice results

Masses from supersymmetric models match continuum values more quickly with new discretizations

SLAC derivative achieves high-accuracy results even without improvement terms

Abstract

We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to discretizations of surface integrals. In one dimension, our simulations show that a model with the Wilson derivative and the Stratonovitch prescription for this discretization leads to far better results at finite lattice spacing than other models with Wilson fermions considered in the literature. In particular, we check that fermionic and bosonic masses coincide and the unbroken Ward identities are fulfilled to high accuracy. Equally good results for the effective masses can be obtained in a model with the SLAC derivative (even without improvement terms). In two dimensions we introduce a non-standard Wilson term in such a way that the discretization errors of the kinetic terms are only of order O(a^2). Masses extracted from the corresponding manifestly supersymmetric model prove to approach their continuum values much quicker than those from a model containing the standard Wilson term. Again, a comparable enhancement can be achieved in a theory using the SLAC derivative.