Massless chiral supermultiplets of higher spins and theθ-twistor

Abstract

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