Journal of High Energy Physics (Sep 2019)
Weak separation, positivity and extremal Yangian invariants
Abstract
Abstract We classify all positive n-particle NkMHV Yangian invariants in N $$ \mathcal{N} $$ = 4 YangMills 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. 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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