On hidden symmetries of a super gauge theory and twistor string theory

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the M-extented self-dual super Yang-Mills equations for general N <= 4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the M-extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded abelian symmetries. We also show that the open topological B-model with the enhanced supertwistor space as target manifold will describe the hierarchies. Furthermore, these hierarchies will in turn - by a supersymmetric extension of Ward's conjecture - reduce to the super hierarchies of integrable models in D < 4 dimensions.