The Yangian origin of the Grassmannian integral

TL;DR

This paper demonstrates that Yangian symmetry uniquely determines the cyclic structure of Grassmannian integrals used to compute scattering amplitudes in N=4 super Yang-Mills theory, highlighting the deep algebraic symmetry underlying the formulas.

Contribution

It shows that Yangian symmetry uniquely constrains the cyclic structure of Grassmannian integral formulas for scattering amplitudes.

Findings

Yangian invariance is confirmed for Grassmannian integrals.

Yangian symmetry uniquely determines the cyclic structure.

The structure is essential for the symmetry of the amplitude formulas.

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.