Symbol alphabets from tensor diagrams
Abstract We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n-particle amplitudes in planar N $$ \mathcal{N} $$ = 4 Yang-Mills theory and certain polytopes associated to the Grassmannian Gr(4, n). We show how to assign a web (...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-12-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2021)079 |
| _version_ | 1818873640117075968 |
|---|---|
| author | Lecheng Ren Marcus Spradlin Anastasia Volovich |
| author_facet | Lecheng Ren Marcus Spradlin Anastasia Volovich |
| author_sort | Lecheng Ren |
| collection | DOAJ |
| description | Abstract We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n-particle amplitudes in planar N $$ \mathcal{N} $$ = 4 Yang-Mills theory and certain polytopes associated to the Grassmannian Gr(4, n). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner we reproduce the results of previous analyses of n ≤ 8, and find that the polytope C † 4 9 $$ {\mathcal{C}}^{\dagger}\left(4,9\right) $$ encodes all rational letters, and all square roots of the algebraic letters, of known nine-particle amplitudes. |
| first_indexed | 2024-12-19T12:57:55Z |
| format | Article |
| id | doaj.art-20face143e4f43dc9547cf4f0f627f75 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T12:57:55Z |
| publishDate | 2021-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-20face143e4f43dc9547cf4f0f627f752022-12-21T20:20:21ZengSpringerOpenJournal of High Energy Physics1029-84792021-12-0120211214310.1007/JHEP12(2021)079Symbol alphabets from tensor diagramsLecheng Ren0Marcus Spradlin1Anastasia Volovich2Department of Physics, Brown UniversityDepartment of Physics, Brown UniversityBrown Theoretical Physics Center, Brown UniversityAbstract We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n-particle amplitudes in planar N $$ \mathcal{N} $$ = 4 Yang-Mills theory and certain polytopes associated to the Grassmannian Gr(4, n). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner we reproduce the results of previous analyses of n ≤ 8, and find that the polytope C † 4 9 $$ {\mathcal{C}}^{\dagger}\left(4,9\right) $$ encodes all rational letters, and all square roots of the algebraic letters, of known nine-particle amplitudes.https://doi.org/10.1007/JHEP12(2021)079Scattering AmplitudesSupersymmetric Gauge Theory |
| spellingShingle | Lecheng Ren Marcus Spradlin Anastasia Volovich Symbol alphabets from tensor diagrams Journal of High Energy Physics Scattering Amplitudes Supersymmetric Gauge Theory |
| title | Symbol alphabets from tensor diagrams |
| title_full | Symbol alphabets from tensor diagrams |
| title_fullStr | Symbol alphabets from tensor diagrams |
| title_full_unstemmed | Symbol alphabets from tensor diagrams |
| title_short | Symbol alphabets from tensor diagrams |
| title_sort | symbol alphabets from tensor diagrams |
| topic | Scattering Amplitudes Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP12(2021)079 |
| work_keys_str_mv | AT lechengren symbolalphabetsfromtensordiagrams AT marcusspradlin symbolalphabetsfromtensordiagrams AT anastasiavolovich symbolalphabetsfromtensordiagrams |