Species Doublers as Super Multiplet Partners in Lattice Supersymmetry

TL;DR

This paper introduces a new lattice superfield formalism that incorporates species doublers as super multiplets, achieving exact supersymmetry in a one-dimensional N=2 model with interactions.

Contribution

It presents a novel lattice superfield formalism in momentum space that treats species doublers as super multiplets, enabling exact lattice supersymmetry.

Findings

Exact supersymmetry achieved for all super charges in the model.

Supersymmetric Ward identities hold at one loop level.

The formalism uses a non local 'star' product to satisfy Leibnitz rule.

Abstract

We propose a new lattice superfield formalism in momentum representation which accommodates species doublers of the lattice fermions and their bosonic counterparts as super multiplets. We explicitly show that one dimensional $N=2$ model with interactions has exact supersymmetry on the lattice for all super charges with lattice momentum. In coordinate representation the finite difference operator is made to satisfy Leibnitz rule by introducing a non local product, the "star" product, and the exact lattice supersymmetry is realized. Supersymmetric Ward identities are shown to be satisfied at one loop level.