Massless Chiral Supermultiplets of Higher Spins and the $\theta$-Twistor

Abstract

Recently N. Berkovits, motivated by the supertwistor description of $\mathcal{N}=4D=4$ super Yang-Mills, considered the generalization of the $\mathcal{N}=1D=4$ $\theta$-twistor construction to D=10 and applied it for a compact covariant description of $\mathcal{N}=1D=10$ 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 $\mathcal{N}=1D=4$ 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 $\mathcal{N}=4D=4$ and can be used for an off-shell description of the corresponding super Yang-Mills theory.

15 pages

References in corpus (3)

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• Ten-Dimensional Super-Twistors and Super-Yang-Mills
• Unification of twistors and Ramond vectors