On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory

Abstract

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N\leq4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the N-extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded Abelian symmetries. We also show that the open topological B-model with the enhanced supertwistor space as target manifold will describe the hierarchies. Furthermore, these hierarchies will in turn -- by a supersymmetric extension of Ward's conjecture -- reduce to the super hierarchies of integrable models in D<4 dimensions.

v3: 1+68 pages, harvmac, typos fixed and one comment added

References in corpus (16)

• Bethe Ansatz for Quantum Strings
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• Conformal Supergravity in Twistor-String Theory
• Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly
• Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory
• Integrability in QCD and beyond
• Non-MHV Tree Amplitudes in Gauge Theory
• Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
• Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions
• Multigluon amplitudes, $\mathcal{N}=4$ constraints and the WZW model
• Quantum string integrability and AdS/CFT
• The Topological B-Model on Fattened Complex Manifolds and Subsectors of N=4 Self-Dual Yang-Mills Theory
• Supertwistors and Cubic String Field Theory for Open N=2 Strings
• Supertwistor Orbifolds: Gauge Theory Amplitudes and Topological Strings
• N=1 Conformal Supergravity and Twistor-String Theory

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• Noncommutative Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
• Symmetries of the Self-Dual Sector of N=4 Super Yang-Mills on the Light Cone
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