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

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

2006-08-31

arxiv.org/abs/hep-th/0608225v1

Commun.Math.Phys.275:685-708,2007

Physics

High Energy Physics

High Energy Physics - Theory

24 pages

Scientific paper

10.1007/s00220-007-0296-1

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.

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