Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

TL;DR

The paper shows that tree-level, planar scattering amplitudes in N=4 SYM possess a Yangian symmetry arising from the combination of conventional and dual superconformal algebras. By formulating amplitudes in on-shell superspace and introducing dual coordinates, the authors construct level-1 Yangian generators and prove their compatibility with the level-0 algebra via bilocal constructions, including a matrix representation. This Yangian structure mirrors the integrable spin-chain picture found in the spectrum, suggesting the amplitude S-matrix inherits intrinsic integrability properties. The work also discusses cyclicity, twistor-space perspectives, and potential deformations at loop level, framing a path toward deeper constraints on amplitudes in this maximally supersymmetric theory.

Abstract

Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a 'dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar N=4 super Yang-Mills, at least at tree level.