Yangian-type symmetries of non-planar leading singularities

TL;DR

This paper explores the presence of Yangian-type symmetries in non-planar scattering amplitudes within N=4 super Yang-Mills theory, revealing partial invariance and new integrable identities related to non-planar geometries.

Contribution

It introduces the action of Yangian generators on non-planar on-shell diagrams and uncovers higher-level symmetries that persist despite breaking of full invariance.

Findings

Higher-level Yangian generators annihilate non-planar diagrams.

Number of preserved generators depends on non-planarity degree.

Identifies integrable transfer matrix identities for non-planar configurations.

Abstract

We take up the study of integrable structures behind non-planar contributions to scattering amplitudes in N=4 super Yang-Mills theory. Focusing on leading singularities, we derive the action of the Yangian generators on color-ordered subsets of the external states. Each subset corresponds to a single boundary of the non-planar on-shell diagram. While Yangian invariance is broken, we find that higher-level Yangian generators still annihilate the non-planar on-shell diagram. For a given diagram, the number of these generators is governed by the degree of non-planarity. Furthermore, we present additional identities involving integrable transfer matrices. In particular, for diagrams on a cylinder we obtain a conservation rule similar to the Yangian invariance condition of planar on-shell diagrams. To exemplify our results, we consider a five-point MHV on-shell function on a cylinder.