Lattice formulation of N=4 super Yang-Mills theory

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We construct a lattice action for 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 N=4 super Yang-Mills theory due to Marcus. Using the discretization prescription developed in an earlier paper on the N=2 theory in two dimensions we are able to translate this geometrical action to the lattice.