{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-study-in-mathbb-g-mathbb-r-geq-0-from-the","title":"A study in $\\mathbb{G}_{\\mathbb{R}, \\geq 0}$: from the geometric case book of Wilson loop diagrams and SYM $N=4$","arxiv_id":"1803.00958","date":"2018-03-02","proceeding":null,"authors":["Susama Agarwala","Sian Fryer"],"abstract":"We study the geometry underlying the Wilson loop diagram approach to calculating scattering amplitudes in the gauge theory of Supersymmetric Yang Mills (SYM) $N=4$. By applying the tools developed to study total positivity in the real Grassmannian, we are able to systematically compute with all Wilson loop diagrams of a given size and find unexpected patterns and relationships between them. We focus on the smallest nontrivial multi-propagator case, consisting of 2 propagators on 6 vertices, and compute the positroid cells associated to each diagram and the homology of the subcomplex they generate in $\\mathbb{G}_{\\mathbb{R}, \\geq 0}$. We also verify in this case the conjecture that the spurious singularities of the volume functional {\\em do} all cancel on the codimension 1 boundaries of these cells.","url_abs":"https://arxiv.org/abs/1803.00958v1","url_pdf":"https://arxiv.org/pdf/1803.00958v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-study-in-mathbb-g-mathbb-r-geq-0-from-the","repo_url":"https://github.com/sianfryer/positroids","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-study-in-mathbb-g-mathbb-r-geq-0-from-the","repo_url":"https://github.com/zeefryer/positroids","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}