Yangians, Grassmannians and T-duality

TL;DR

This paper explores the Yangian symmetry in N=4 super Yang-Mills theory, demonstrating its relation to T-duality and proving invariance of Grassmannian integral formulas for scattering amplitudes.

Contribution

It establishes the equivalence of twistor and momentum twistor formulations of Yangian symmetry and proves the Yangian invariance of Grassmannian integral formulas.

Findings

Yangian symmetry can be interchanged between twistor and momentum twistor space.

The full symmetry is the Yangian of the dual superconformal algebra.

Grassmannian integral formulas are proven to be Yangian invariant.

Abstract

We investigate the Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out. The equivalence of this picture with the one where the ordinary superconformal symmetry is thought of as fundamental is an algebraic expression of T-duality. Motivated by this, we analyse some recently proposed formulas, which reproduce different contributions to amplitudes through a Grassmannian integral. We prove their Yangian invariance by directly applying the generators.