{"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/towards-a-complete-classification-of-6d","title":"Towards a complete classification of 6D supergravities","arxiv_id":"2311.00868","date":"2023-11-01","proceeding":null,"authors":["Yuta Hamada","Gregory J. Loges"],"abstract":"The constraints arising from anomaly cancellation are particular strong for chiral theories in six dimensions. We make progress towards a complete classification of 6D supergravities with minimal supersymmetry and non-abelian gauge group. First, we generalize a previously known infinite class of anomaly-free theories which has $T\\gg 9$ to essentially any semi-simple gauge group and infinitely many choices for hypermultiplets. The construction relies on having many decoupled sectors all selected from a list of four simple theories which we identify. Second, we use ideas from graph theory to rephrase the task of finding anomaly-free theories as constructing cliques in a certain multigraph. A branch-and-bound type algorithm is described which can be used to explicitly construct, in a $T$-independent way, anomaly-free theories with an arbitrary number of simple factors in the gauge group. We implement these ideas to generate an ensemble of $\\mathcal{O}(10^7)$ irreducible cliques from which anomaly-free theories may be easily built, and as a special case obtain a complete list of $19,\\!847$ consistent theories for $T=0$, for which the maximal gauge group rank is $24$. Modulo $\\mathrm{U}(1)$, $\\mathrm{SU}(2)$ and $\\mathrm{SU}(3)$ simple factors and the new infinite families, we give a complete characterization of anomaly-free theories and show that the bound $T\\leq 273$ is sharp.","url_abs":"https://arxiv.org/abs/2311.00868v3","url_pdf":"https://arxiv.org/pdf/2311.00868v3.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":"towards-a-complete-classification-of-6d","repo_url":"https://github.com/gloges/6d-sugra-classify","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"towards-a-complete-classification-of-6d","repo_url":"https://github.com/gloges/6d-sugra-data","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}