Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2

TL;DR

This paper introduces a novel lattice superfield formalism that incorporates species doublers as super multiplets, achieving exact supersymmetry with interactions in a one-dimensional N=2 model through a nonlocal product and sine momentum conservation.

Contribution

It presents a new formalism for lattice supersymmetry that treats species doublers as super multiplets and maintains exact supersymmetry with interactions in D=1 N=2 models.

Findings

Exact lattice supersymmetry achieved for all super charges.

Supersymmetric Ward identities verified at one loop.

Connection established with Hopf algebraic structures.

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 Lie algebraic supersymmetry on the lattice for all super charges. 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. The standard momentum conservation is replaced on the lattice by the conservation of the sine of the momentum, which plays a crucial role in the formulation. Half lattice spacing structure is essential for the one dimensional model and the lattice supersymmetry transformation can be identified as a half lattice spacing translation combined with alternating sign structure. Invariance under finite translations and locality in the continuum limit are explicitly investigated and shown to be recovered. Supersymmetric Ward identities are shown to be satisfied at one loop level. Lie algebraic lattice supersymmetry algebra of this model suggests a close connection with Hopf algebraic exactness of the link approach formulation of lattice supersymmetry.