Ten-dimensional super-twistors and Super-Yang-Mills

Abstract

Four-dimensional super-twistors provide a compact covariant description of on-shell $\mathcal{N}{ = 4}$ d=4 super-Yang-Mills. In this paper, ten-dimensional super-twistors are introduced which similarly provide a compact covariant description of on-shell d=10 super-Yang-Mills. The super-twistor variables are Z = (λ^α, μ_α, Γ^m) where λ^α and μ_α are constrained bosonic d=10 spinors and Γ^m is a constrained fermionic d=10 vector. The Penrose map relates the twistor superfield Φ(Z) with the d=10 super-Yang-Mills vertex operator λ^α A _α(x, θ) which appears in the pure spinor formalism of the superstring, and the cubic super-Yang-Mills amplitude is proportional to the super-twistor integral ∫ dZ Φ1Φ2Φ3.