Species Doublers as Super Multiplets in Lattice Supersymmetry: Chiral Conditions of Wess-Zumino Model for D=N=2

TL;DR

This paper develops an algebraic lattice supersymmetry framework that preserves exact supersymmetry, addresses chiral fermion issues, and introduces a novel product to maintain Leibnitz rule, with nonlocality diminishing in the continuum limit.

Contribution

It presents a new algebraic formulation of lattice supersymmetry that incorporates species doublers into supermultiplets and maintains exact supersymmetry.

Findings

Lattice chiral conditions can be imposed to preserve supersymmetry.

Species doublers are incorporated into supermultiplets, solving the chiral fermion problem.

Nonlocal interactions arise but become negligible in the continuum limit.

Abstract

We propose an algebraic lattice supersymmetry formulation which has an exact supersymmetry on the lattice. We show how lattice version of chiral conditions can be imposed to satisfy an exact lattice supersymmetry algebra. The species doublers of chiral fermions and the corresponding bosonic counterparts can be accommodated to fit into chiral supermultiplets of lattice supersymmetry and thus lattice chiral fermion problem does not appear. We explicitly show how N=2 Wess-Zumino model in one and two dimensions can be formulated to keep exact supersymmetry for all super charges on the lattice. The momentum representation of N=2 lattice chiral sypersymmetry algebra has lattice periodicity and thus momentum conservation should be modified to a lattice version of sine momentum conservation, which generates nonlocal interactions and leads to a loss of lattice translational invariance. It is shown that the nonlocality is mild and the translational invariance is recovered in the continuum limit. In the coordinate representation a new type of product is defined and the difference operator satisfies Leibnitz rule and an exact lattice supersymmetry is realized on this product.