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

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.