On Supertwistors, the Penrose-Ward Transform and N=4 super Yang-Mills Theory

Abstract

It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP^{3|4} as a target space is equivalent to holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in turn is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual N-extended SYM theory as the integrability of super Yang-Mills fields on complex (2|N)-dimensional superplanes and demonstrate the equivalence of this description to Witten's formulation. The equivalence of the field equations of hCS theory on an open subset of CP^{3|N} to the field equations of self-dual N-extended SYM theory in four dimensions is made explicit. Furthermore, we extend the picture to the full N=4 SYM theory and, by using the known supertwistor description of this case, we show that the corresponding constraint equations are (gauge) equivalent to the field equations of hCS theory on a quadric in CP^{3|3}xCP^{3|3}.

arXiv comment48 pages; version to appear in ATMP

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• The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory
• Orbifolding the Twistor String
• The Topological B-Model on Fattened Complex Manifolds and Subsectors of N=4 Self-Dual Yang-Mills Theory
• Matrix Models and D-branes in Twistor String Theory
• Gauge Theory Amplitudes, Scalar Graphs and Twistor Space
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• A Six Dimensional View on Twistors
• N=1 Conformal Supergravity and Twistor-String Theory
• A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory
• Ricci-flat supertwistor spaces
• Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory
• Yang-Mills gravity in biconformal space