Lattice Formulation of {\cal N}=4 Super Yang-Mills Theory

We construct a lattice action for {\cal N}=4 super Yang-Mills theory in four dimensions which is local, gauge invariant, free of spectrum doubling and possesses a single exact supersymmetry. Our construction starts from the observation that the fermions of the continuum theory can be mapped into the component fields of a single real anticommuting Kahler-Dirac field. The original supersymmetry algebra then implies the existence of a nilpotent scalar supercharge Q and a corresponding set of bosonic superpartners. Using this field content we write down a Q-exact action and show that, with an appropriate change of variables, it reduces to a well-known twist of {\cal N}=4 super Yang-Mills theory due to Marcus. Using the discretization prescription developed in an earlier paper on the {\cal N}=2 theory in two dimensions we are able to translate this geometrical action to the lattic