Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions

We propose a lattice formulation of three dimensional super Yang-Mills model with a twisted N=4 supersymmetry. The extended supersymmetry algebra of all the eight supercharges is fully and exactly realized on the lattice with a modified "Leibniz rule". The formulation we employ here is a three dimensional extension of manifestly gauge covariant method which was developed in our previous proposal of Dirac-Kaehler twisted N=2 super Yang-Mills on two dimensional lattice. The twisted N=4 supersymmetry algebra is geometrically realized on a three dimensional lattice with link supercharges and the use of "shifted" (anti-)commutators. A possible solution to the recent critiques on the link formulation will be discussed.