Massless chiral supermultiplets of higher spins and the θ-twistor

Recently N. Berkovits, motivated by the supertwistor description of N = 4 D = 4 super Yang-Mills, considered the generalization of the N = 1 D = 4 theta-twistor construction to D = 10 and applied it for a compact covariant description of N = 1 D = 10 super Yang-Mills. This supports the relevance of the theta-twistor as a supersymmetric twistor alternative to the well-known supertwistor. The minimal breaking of superconformal symmetry is an inherent property of the theta-twistor received from its fermionic components, described by a Grassmannian vector instead of a Grassmannian scalar in the supertwistor. The theta-twistor description of the N = 1 D = 4 massless chiral supermultiplets (S, S + 1/2) with spins S = 0, 1/2, 1, 3/2, 2, ... is considered here. The description permits to restore the auxiliary F fields of the chiral supermultiplets absent in the supertwistor approach. The proposed formalism is naturally generalized to N = 4 D = 4 and can be used for an off-shell description of the corresponding super Yang-Mills theory.