Cluster Adjacency for m=2 Yangian Invariants

TL;DR

This paper classifies and explicitly enumerates all rational Yangian invariants in a toy model of N=4 Yang-Mills theory, revealing their cluster adjacency properties within the amplituhedron framework.

Contribution

It provides a complete classification and explicit formula for Yangian invariants in the m=2 model, highlighting their cluster adjacency in the amplituhedron.

Findings

All invariants satisfy cluster adjacency with respect to Gr(2,n)

Explicit enumeration and formula for invariants for any n and k

Connection between invariants and generalized triangles in the amplituhedron

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.