Weak separation, positivity and extremal Yangian invariants
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 know...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2019)093 |
| Summary: | 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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| ISSN: | 1029-8479 |