Cluster Adjacency for m=2 Yangian Invariants

Abstract

We classify the rational Yangian invariants of the $m=2$ toy model of $\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the amplituhedron ${\mathcal{A}}_{n,k}^{(2)}$. We enumerate and provide an explicit formula for all invariants for any number of particles $n$ and any helicity degree $k$. Each invariant manifestly satisfies cluster adjacency with respect to the $Gr(2,n)$ cluster algebra.

arXiv comment11 pages, 3 figures

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• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry
• Triangulations and Canonical Forms of Amplituhedra: a fiber-based approach beyond polytopes
• A Note on One-loop Cluster Adjacency in N = 4 SYM
• The Amplituhedron BCFW Triangulation
• BCFW tilings and cluster adjacency for the amplituhedron