Yangian-type symmetries of non-planar leading singularities

We take up the study of integrable structures behind non-planar contributions to scattering amplitudes in $$ mathcal{n}=4 $$ 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.