Hidden Symmetries and Integrable Hierarchy of the N = 4 Supersymmetric Yang-Mills Equations

2006/08/31 by Alexander D. Popov, Martin Wolf · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Generalization #Hierarchy #Homogeneous space #Infinite set #Integrable system #Nonlinear Waves and Solitons #Quantum #Space (punctuation) #Supersymmetry #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/s00220-007-0296-1

published as Commun.Math.Phys.275:685-708,2007 · 24 pages

arxiv created 2006/08/31 · openalex publication_date 2007/08/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the N=4 SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solving the equations of the hierarchy. We embed the N=4 SYM equations in the infinite system of the hierarchy equations and show that this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations. Presumably, the existence of such nonlocal symmetries underlies the observed integrable structures in quantum N=4 SYM theory.

Citations

• Marginal deformations of N=4 SYM from open/closed twistor strings
• N=2 (4) string theory is self-dualN=4 Yang-Mills theory
• Extended conformal symmetries of the self-dual Yang-Mills equations
• Matrix models and D-branes in twistor string theory
• Supertwistors and cubic string field theory for open N=2 strings
• Perturbative Gauge Theory As A String Theory In Twistor Space

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