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 |
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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 |
| _version_ | 1828797550142947328 |
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| author | Luke Lippstreu Jorge Mago Marcus Spradlin Anastasia Volovich |
| author_facet | Luke Lippstreu Jorge Mago Marcus Spradlin Anastasia Volovich |
| author_sort | Luke Lippstreu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T04:42:21Z |
| format | Article |
| id | doaj.art-6d34bfa0332d448caedea4dbf0cb05bd |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T04:42:21Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-6d34bfa0332d448caedea4dbf0cb05bd2022-12-22T00:37:45ZengSpringerOpenJournal of High Energy Physics1029-84792019-09-012019911710.1007/JHEP09(2019)093Weak separation, positivity and extremal Yangian invariantsLuke Lippstreu0Jorge Mago1Marcus Spradlin2Anastasia Volovich3Department of Physics, Brown UniversityDepartment of Physics, Brown UniversityDepartment of Physics and Brown Theoretical Physics Center, Brown UniversityDepartment of Physics, Brown UniversityAbstract 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.http://link.springer.com/article/10.1007/JHEP09(2019)093Scattering AmplitudesSupersymmetric Gauge Theory |
| spellingShingle | Luke Lippstreu Jorge Mago Marcus Spradlin Anastasia Volovich Weak separation, positivity and extremal Yangian invariants Journal of High Energy Physics Scattering Amplitudes Supersymmetric Gauge Theory |
| title | Weak separation, positivity and extremal Yangian invariants |
| title_full | Weak separation, positivity and extremal Yangian invariants |
| title_fullStr | Weak separation, positivity and extremal Yangian invariants |
| title_full_unstemmed | Weak separation, positivity and extremal Yangian invariants |
| title_short | Weak separation, positivity and extremal Yangian invariants |
| title_sort | weak separation positivity and extremal yangian invariants |
| topic | Scattering Amplitudes Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP09(2019)093 |
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