Lattice Supersymmetry: Some Ideas from Low Dimensional Models

TL;DR

This paper explores implementing exact N=1 supersymmetry on a lattice using the link approach, revealing a non-local action and interpreting boson-fermion relations as species doublers in a low-dimensional model.

Contribution

It introduces a novel lattice formulation of N=1 supersymmetry in one dimension that maintains exact supersymmetry through a momentum-space approach.

Findings

Lattice with spacing a/2 doubles the sites compared to conventional models.

Supersymmetry relates bosons and fermions via a 2pi/a momentum shift.

The resulting lattice action is non-local in coordinate space.

Abstract

In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites as the conventional one. The boson and fermion are related through a 2pi/a momentum shift, which can provide an interpretation of them being species doublers to each other. An exactly supersymmetric lattice action can be written within this scheme in momentum representation, which however turns out to be non local in coordinate space.