Twisted superspace on a lattice Original Research Article

We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of image twisted supersymmetry invariant BF and Wess–Zumino models in two dimensions. We introduce mild lattice non-commutativity to preserve Leibniz rule on the lattice. The formulation is based on the twisted superspace formalism for image supersymmetry which was proposed recently. From the consistency condition of the non-commutativity of superspace, we find an unexpected three-dimensional lattice structure which may reduce into two-dimensional lattice where the superspace describes semilocally scattered fermions and bosons within a double size square lattice.