Massless chiral supermultiplets of higher spins and the {theta}-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.