Weak separation, positivity and extremal Yangian invariants

Journal Article · 12 September 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP09(2019)093 · OSTI ID:1594824

Lippstreu, Luke ^[1]; Mago, Jorge ^[2]; Spradlin, Marcus ^[2]; Volovich, Anastasia ^[2]

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1. Brown Univ., Providence, RI (United States); Brown University
2. Brown Univ., Providence, RI (United States)

We classify all positive $$n$$-particle N^kMHV Yangian invariants in $N =$ 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.

• Research Organization: Brown Univ., Providence, RI (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• Grant/Contract Number: SC0010010
• OSTI ID: 1594824
• Report Number(s): arXiv:1906.11034
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2019; ISSN 1029-8479
• Publisher: Springer BerlinCopyright Statement
• Country of Publication: United States
• Language: English