Conserved currents for unconventional supersymmetric couplings of self-dual gauge fields

Self-dual gauge potentials admit supersymmetric couplings to higher-spin fields satisfying interacting forms of the first order Dirac-Fierz equation. The interactions are governed by conserved currents determined by supersymmetry. These super-self-dual Yang-Mills systems provide on-shell supermultiplets of arbitrarily extended super-Poincaré algebras; classical consistency not setting any limit on the extension N. We explicitly display equations of motion up to the N = 6 extension. The stress tensor, which vanishes for the N ≤ 3 self-duality equations, not only gets resurrected when N = 4, but is then a member of a conserved multiplet of gauge-invariant tensors.