Non-Abelian Born–Infeld and kappa-symmetry

We define an iterative procedure to obtain a non-Abelian generalization of the Born–Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. In this paper we will present all bosonic terms in the action up to terms quartic in the Yang–Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric trace-prescription.