Ginsparg–Wilson relation and lattice supersymmetry

The Ginsparg–Wilson (GW) relation is extended for supersymmetric free theories on a lattice. Exact lattice supersymmetry (SUSY) can be defined without any ambiguities in difference operators. The lattice action constructed by a block-spin transformation is invariant under the symmetry. U(1)R symmetry on the lattice is also realized as one of exact symmetries. For an application, the extended GW relation is given for a two-dimensional model with chiral-multiplets. It is argued that the relation may be generalized for interacting cases.