Interacting fields of arbitrary spin andN >4 supersymmetric selfdual Yang-Mills equations

We show that the self-dual Yang-Mills equations afford supersymmetrisation to systems of equations invariant under global N-extended super-Poincar\'e transformations for arbitrary values of N, without the limitation (N\le 4) applicable to standard non-self-dual Yang-Mills theories. These systems of equations provide novel classically consistent interactions for vector supermultiplets containing fields of spin up to (N-2)/2. The equations of motion for the component fields of spin greater than 1/2 are interacting variants of the first-order Dirac--Fierz equations for zero rest-mass fields of arbitrary spin. The interactions are governed by conserved currents which are constructed by an iterative procedure. In (arbitrarily extended) chiral superspace, the equations of motion for the (arbitrarily large) self-dual supermultiplet are shown to be completely equivalent to the set of algebraic supercurvature constraints defining the self-dual superconnection.