We have recently proposed a new lattice SUSY formulation which has exact lattice supersymmetry for Wess-Zumino models in one and two dimensions for all N=2 supercharges. This formulation is non-local in the coordinate space but the difference operato
r satisfies the Leibniz rule on the newly defined star product. Here we show that this lattice supersymmetry is kept exact at the quantum level by investigating Ward-Takahashi identities up to two loop level.
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 chir
al 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.
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 interact
ions 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.
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 interactio
ns 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.
