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