Yangian Symmetry for the Tree Amplituhedron

TL;DR

This paper establishes a connection between Yangian symmetry and the tree-level amplituhedron in planar N=4 super Yang-Mills theory, providing a new geometric understanding of scattering amplitudes through integrability.

Contribution

It introduces a method to construct amplituhedron volume forms from an underlying spin chain, extending Yangian invariance to the amplituhedron framework.

Findings

Constructed amplituhedron volume forms using integrable spin chain methods

Proposed a novel on-shell diagrammatics for the amplituhedron

Clarified the role of Yangian invariance in the geometric structure

Abstract

Tree-level scattering amplitudes in planar N=4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows to obtain a general, explicit method to find such invariants. The uplifting of this result to the amplituhedron construction has been an important open problem. In this paper, with the help of methods proper to integrable theories, we successfully fill this gap and clarify the meaning of Yangian invariance for the tree-level amplituhedron. In particular, we construct amplituhedron volume forms from an underlying spin chain. As a by-product of this construction, we also propose a novel on-shell diagrammatics for the amplituhedron.