Yangian Symmetry for the Tree Amplituhedron

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.

17 pages, 4 figures; v2: extended discussion of results, minor typos corrected, version published in Journal of Physics A

References in corpus (6)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• The Yangian origin of the Grassmannian integral
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• Towards the Amplituhedron Volume
• The Amplituhedron and the One-loop Grassmannian Measure

Cited by in corpus (9)

• Cluster Adjacency for m=2 Yangian Invariants
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Amplituhedron meets Jeffrey-Kirwan Residue
• Amplituhedra, and Beyond
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• All-loop cuts from the Amplituhedron
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• Non-planar BCFW Grassmannian Geometries
• Poles At Infinity in On-shell Diagrams