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

TL;DR

This paper explores the use of the $ heta$-twistor to describe massless chiral supermultiplets of higher spins in supersymmetric theories, offering a covariant framework that includes auxiliary fields and generalizes to extended supersymmetry.

Contribution

It introduces a $ heta$-twistor-based formalism for massless supermultiplets, restoring auxiliary fields and enabling off-shell descriptions, extending previous supertwistor approaches.

Findings

$ heta$-twistor describes supermultiplets with spins 0 to 2 and beyond.

Restores auxiliary $F$ fields absent in supertwistor formalism.

Generalizes to $ ext{N}=4$ supersymmetry for super Yang-Mills theories.

Abstract

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