Higher derivative modifications ofD=10 superspace Yang-Mills theories

We extend the superspace treatment of higher derivative supersymmetric Yang-Mills theories, emphasizing the role played by manifestD=10 Lorentz covariance and supersymmetry invariance. As an example, the superspace formulation of the effective action is considered for the massless fields in the open superstring, as well as in theSO(32) andE ₈×E₈ superstring theories. We show that there exists a unique modification of thef-tensor supercurrent which can provide the embedding of theO(α'³) string corrections in the slope parameter expansion for the Yang-Mills sector inD=10 superspace. The new correction term is relevant for the understanding of nonperturbative effects.