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

Four-dimensional super-twistors provide a compact covariant description of on-shell 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 - (lambda(alpha), mu(alpha), Gamma(m)) where lambda(alpha) and mu(alpha) are constrained bosonic d=10 spinors and Gamma(m) is a constrained fermionic d=10 vector. The Penrose map relates the twistor superfield Phi(Z) with the d=10 super-Yang-Mills vertex operator lambda(alpha) A(alpha)(x,theta) which appears in the pure spinor formalism of the superstring, and the cubic super-Yang-Mills amplitude is proportional to the super- twistor integral f dZ Phi(1)Phi(2)Phi(3).