Weak Separation, Positivity and Extremal Yangian Invariants
arXiv:1906.11034 · doi:10.1007/JHEP09(2019)093
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.
arXiv comment19 pages, 7 figures; v2: minor changes
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