Complete supersymmetry on the lattice and a No-Go theorem

In this work a lattice formulation of a supersymmetric theory is proposed and tested that preserves the complete supersymmetry on the lattice. The results of a one-dimensional nonperturbative simulation show the realization of the full supersymmetry and the correct continuum limit of the theory. It is proven here that the violation of supersymmetry due to the absence of the Leibniz rule on the lattice can be amended only with a nonlocal derivative and nonlocal interaction term. The fermion doubling problem is also discussed, which leads to another important source of supersymmetry breaking on the lattice. This problem is also solved with a nonlocal realization.