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arXiv · 1906.11034

Weak Separation, Positivity and Extremal Yangian Invariants

Luke Lippstreu·Jorge Mago·Marcus Spradlin·Anastasia Volovich
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Abstract

We classify all positive n-particle N^kMHV Yangian invariants in N=4 Yang-Mills theory with n=5k, which we call extremal because none exist for n>5k. We show that this problem is equivalent to that of enumerating plane cactus graphs with k pentagons. We use the known solution of that problem to provide an exact expression for the number of cyclic classes of such invariants for any k, and a simple rule for writing them down explicitly. As a byproduct, we provide an alternative (but equivalent) classification by showing that a product of k five-brackets with disjoint sets of indices is a positive Yangian invariant if and only if the sets are all weakly separated.

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Luke Lippstreu, Jorge Mago, Marcus Spradlin, Anastasia Volovich. 2019-06-26. Weak Separation, Positivity and Extremal Yangian Invariants. https://doi.org/10.1007/jhep09(2019)093

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