{"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/genus-drop-in-hyperelliptic-feynman-integrals","title":"Genus Drop in Hyperelliptic Feynman Integrals","arxiv_id":"2307.11497","date":"2023-07-21","proceeding":null,"authors":["Robin Marzucca","Andrew J. McLeod","Ben Page","Sebastian Pögel","Stefan Weinzierl"],"abstract":"The maximal cut of the nonplanar crossed box diagram with all massive internal propagators was long ago shown to encode a hyperelliptic curve of genus 3 in momentum space. Surprisingly, in Baikov representation, the maximal cut of this diagram only gives rise to a hyperelliptic curve of genus 2. To show that these two representations are in agreement, we identify a hidden involution symmetry that is satisfied by the genus 3 curve, which allows it to be algebraically mapped to the curve of genus 2. We then argue that this is just the first example of a general mechanism by means of which hyperelliptic curves in Feynman integrals can drop from genus $g$ to $\\lceil g/2 \\rceil$ or $\\lfloor g/2 \\rfloor$, which can be checked for algorithmically. We use this algorithm to find further instances of genus drop in Feynman integrals.","url_abs":"https://arxiv.org/abs/2307.11497v1","url_pdf":"https://arxiv.org/pdf/2307.11497v1.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":"genus-drop-in-hyperelliptic-feynman-integrals","repo_url":"https://gitlab.com/s.poegel/algebraiccurves","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"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}