Massless Chiral Supermultiplets of Higher Spins and the θ-Twistor

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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 θ-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 θ-twistor as a supersymmetric twistor alternative to the well-known supertwistor. The minimal breaking of superconformal symmetry is an inherent property of the θ-twistor received from its fermionic components, described by a Grassmannian vector instead of a Grassmannian scalar in the supertwistor. The θ-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.