Ten-Dimensional Super-Twistors and Super-Yang-Mills

TL;DR

This paper introduces ten-dimensional super-twistors that offer a compact, covariant framework for describing on-shell ten-dimensional super-Yang-Mills theory, extending the four-dimensional super-twistor formalism.

Contribution

The paper develops a ten-dimensional super-twistor formalism that parallels the four-dimensional case, providing a new covariant description of on-shell super-Yang-Mills in ten dimensions.

Findings

Super-twistor variables are defined for d=10 super-Yang-Mills.

The Penrose map relates super-twistor superfields to super-Yang-Mills vertex operators.

Cubic super-Yang-Mills amplitudes are expressed as super-twistor integrals.

Abstract

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 \int dZ Phi_1 Phi_2 Phi_3.