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

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.

14 pages harvmac, added short clarification

References in corpus (4)

• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Explaining the Pure Spinor Formalism for the Superstring
• Covariant representation theory of the Poincaré algebra and some of its extensions
• Unification of twistors and Ramond vectors

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• Pure spinors, twistors, and emergent supersymmetry
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• Supertwistor formulation for massless superparticle in $Ad{S}_5\times S^5$ superspace
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Superforms in Simple Six-dimensional Superspace
• Taming the 11D pure spinor b-ghost
• Supermultiplet of $\beta -$deformations from twistors
• On possible composite structure of scalar fields in expanding universe
• Massless Chiral Supermultiplets of Higher Spins and the $\theta$-Twistor
• A Pure Spinor Twistor Description of Ambitwistor Strings