{"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/the-two-loop-amplituhedron","title":"The two-loop Amplituhedron","arxiv_id":"2410.11501","date":"2024-10-15","proceeding":null,"authors":["Gabriele Dian","Elia Mazzucchelli","Felix Tellander"],"abstract":"The loop-Amplituhedron $\\mathcal{A}^{(L)}_{n}$ is a semialgebraic set in the product of Grassmannians $\\mathrm{Gr}_{\\mathbb{R}}(2,4)^L$. Recently, many aspects of this geometry for the case of $L=1$ have been elucidated, such as its algebraic and face stratification, its residual arrangement and the existence and uniqueness of the adjoint. This paper extends this analysis to the simplest higher loop case given by the two-loop four-point Amplituhedron $\\mathcal{A}^{(2)}_4$.","url_abs":"https://arxiv.org/abs/2410.11501v2","url_pdf":"https://arxiv.org/pdf/2410.11501v2.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":"the-two-loop-amplituhedron","repo_url":"https://github.com/gabrieledian/loop-amplituhedron-stratification","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}