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We have proposed a lattice SUSY formulation which we may call super doublerapproach, where chiral fermion species doublers and their bosonic counter partsare either identified as super partners or truncated by chiral conditions. Weclaim that the super symmetry is exactly kept on the lattice. However theformulation is nonlocal and breaks lattice translational invariance. We arguethat these features cause no fundamental difficulties in the continuum limit.Although a naive version of this formulation breaks associativity of theproduct of fields we have found a modified super doubler approach that recoversthe associativity and is applicable to super Yang-Mills theory. It turns outthat this formulation is essentially equivalent to the continuum formulationand thus keeps all the symmetry exact even at a finite lattice constant.Inspired by this formulation we propose a non-local lattice field theoryformulation which is free of chiral fermion problem and has the same exactlattice symmetry as continuum theory.

Summary of Super Doubler Approach on Exact Lattice Supersymmetry