{"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/on-classifying-hyperkahler-kummer-8-orbifolds","title":"On Classifying HyperKähler Kummer 8-Orbifolds","arxiv_id":"2501.03692","date":"2025-01-07","proceeding":null,"authors":["Daniel Andrew Baldwin","Bobby Samir Acharya"],"abstract":"HyperK\\\"ahler spaces, including manifolds, orbifolds and conical singularities play an important role in superstring/$M$-theory and gauge theories as well as in differential and algebraic geometry. In this paper we provide hundreds of new examples of compact hyperK\\\"ahler orbifolds of Kummer type $T^8/G$, where $T^8$ is the maximal torus of the compact Lie group $E_8$ and $G$ a finite group of isometries whose holonomies form a subgroup of the Weyl group of $E_8$. We show that, out of all of these examples, the only orbifolds whose singularities have a known holomorphic symplectic resolution lead to manifolds diffeomorphic to the two currently known examples of compact hyperK\\\"ahler 8-manifolds. We also demonstrate that these methods can, when combined with theorems of Joyce, be extended to construct potentially new manifolds of $\\operatorname{SU}(4)$- and $\\operatorname{Spin}(7)$- holonomy. All of these examples give rise to new vacua of string/$M$-theory in two/three dimensions.","url_abs":"https://arxiv.org/abs/2501.03692v1","url_pdf":"https://arxiv.org/pdf/2501.03692v1.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":"on-classifying-hyperkahler-kummer-8-orbifolds","repo_url":"https://github.com/d-a-baldwin/hyperkahler-8mfds","is_official":1,"mentioned_in_paper":1,"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}