The Yangian origin of the Grassmannian integral

TL;DR

The paper proves that the Grassmannian integral form proposed for leading singularities in planar N=4 SYM is uniquely fixed by Yangian invariance under Y(sl(4|4)) when zero homogeneity is enforced. By analyzing invariance under level-one generators, the authors show that any non-constant multiplicative deformation f(t) would break the total-derivative structure of the level-one variation, hence f(t) must be constant almost everywhere, establishing uniqueness of the Arkani-Hamed–Mason–Bullimore–Kapustin form. They also explore what happens when the homogeneity constraints are relaxed, finding possible nontrivial Yas invariant deformations that do not correspond to physical amplitudes in N=4 SYM but illustrate a broader Yangian-invariant landscape. The work solidifies the Grassmannian integral as a canonical, highly symmetric construction for tree-level leading singularities and clarifies the role of contour dependence and T-duality in these formulations.

Abstract

In this paper we analyse formulas which reproduce different contributions to scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian integral. Recently their Yangian invariance has been proved directly by using the explicit expression of the Yangian level-one generators. The specific cyclic structure of the form integrated over the Grassmannian enters in a crucial way in demonstrating the symmetry. Here we show that the Yangian symmetry fixes this structure uniquely.