Deformed matrix models , supersymmetric lattice twists and N = 14 supersymmetry

A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of N = (8, 8) theory on a curved background (a two-sphere) is constructed. Both continuum and the matrix regularization respect four exact scalar supersymmetries under a twisted version of the supersymmetry algebra. We then discuss a succinct Q = 1 deformed matrix model regularization ofN = 4 SYM in d = 4, which is equivalent to a non-commutative A4 orbifold lattice formulation. Motivated by recent progress in supersymmetric lattices, we also propose a N = 1 4 supersymmetry preserving deformation of N = 4 SYM theory on R 4. In this class of N = 14 theories, both the regularized and continuum theory respect the same set of (scalar) supersymmetry. By using the equivalence of the deformed matrix models with the lattice formulations, we give a very simple physical argument on why the exact lattice supersymmetry must be a subset of scalar subalgebra. This argument disagrees with the recent claims of the link approach, for which we give a new interpretation.