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

TL;DR

This paper uncovers an infinite-dimensional algebra of hidden symmetries in N=4 supersymmetric Yang-Mills theory, revealing an integrable hierarchy structure linked to supertwistor methods and recursive symmetries.

Contribution

It introduces a novel integrable hierarchy for N=4 SYM derived from supertwistor correspondence, expanding understanding of its hidden symmetries and integrability.

Findings

Constructed an infinite sequence of flows on the solution space.

Embedded N=4 SYM equations into an integrable hierarchy.

Linked nonlocal symmetries to integrable structures in quantum N=4 SYM.

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.