Supersymmetric self-dual Yang-Mills theories from local nilpotent fermionic symmetry

We present a system of a self-dual vector-spinor and a self-dual Yang-Mills (YM) field with local nilpotent fermionic symmetry (but not supersymmetry) in D = 2 + 2 dimensions that embeds self-dual supersymmetric YM theory as a special set of exact solutions. Our system has local nilpotent fermionic symmetry generator N-alpha(I) satisfying the algebra {N-alpha(I), N-beta(J)} = 0 with the adjoint index t of an arbitrary gauge group. Our original field content in D = 2 + 2 is (A(mu)(I,) psi(I)(mu) ,chi(I)) where A(mu)(I) is the usual YM gauge field, psi(I)(mu) is a Majorana-Weyl vector-spinor gauging N-alpha(I), while chi(I) is a Majorana-Weyl spinor compensator field needed for consistency. This system embeds self -dual supersymmetric YM system with the field content (A(mu)(I) ,lambda_(I)) in D = 2 + 2. As other examples, we consider similar systems in D = 7 + 0 and D = 8 + 0 embedding respectively N = 1/8 + 7/8 and N = (1/8,1) supersymmetric YM theories with generalized self-dualities, such as F-mu nu(I) = (1/2)f(mu nu)(rho sigma) F-rho sigma(I) with a generalized octonionic structure constant f(mu nu)rho sigma. This result strongly suggests that our local nilpotent fermionic symmetry is more fundamental than the supersymmetric self -dual Yang -Mills systems that are supposed to generate all supersymmetric integrable models in D < 4. (C) 2017 The Authors. Published by Elsevier B.V.