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 N=2 twisted supersymmetry invariant BF and Wess-Zumino models in two dimensions. We introduce mild lattice noncommutativity to preserve Leibniz rule on the lattice. The formulation is based on the twisted superspace formalism for N=D=2 supersymmetry which was proposed recently. From the consistency condition of the noncommutativity 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.
@article{arxiv.hep-lat/0406029,
title = {Twisted Superspace on a Lattice},
author = {Alessandro D'Adda and Issaku Kanamori and Noboru Kawamoto and Kazuhiro Nagata},
journal= {arXiv preprint arXiv:hep-lat/0406029},
year = {2014}
}