Every m=2 Yangian invariant is labelled by a collection of non-intersecting polygons in an n-gon, yielding an explicit formula whose denominator factors lie in a common Gr(2,n) cluster, thus manifestly satisfying cluster adjacency.
Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
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abstract
We conjecture that every rational Yangian invariant in N=4 SYM theory satisfies a recently introduced notion of cluster adjacency. We provide evidence for this conjecture by using the Sklyanin Poisson bracket on Gr(4,n) to check numerous examples.
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Cluster Adjacency for m=2 Yangian Invariants
Every m=2 Yangian invariant is labelled by a collection of non-intersecting polygons in an n-gon, yielding an explicit formula whose denominator factors lie in a common Gr(2,n) cluster, thus manifestly satisfying cluster adjacency.