{"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/wilson-loops-holomorphic-anomaly-equations","title":"Wilson loops, holomorphic anomaly equations and blowup equations","arxiv_id":"2305.09171","date":"2023-05-16","proceeding":null,"authors":["Xin Wang"],"abstract":"We investigate the topological string correspondence of the five-dimensional half-BPS Wilson loops on $S^1$. First, we propose the refined holomorphic anomaly equations for the BPS sectors of the Wilson loop expectation values. We then solve these equations and obtain many non-trivial novel integral refined BPS invariants for rank-one models. By studying the Wilson loop expectation values around the conifold point, we obtain the quantum spectra of the quantum Hamiltonians of the associated integrable systems. Lastly, as an application, the study of this paper leads to a generalization of the blowup equations for arbitrary magnetic fluxes that satisfy the flux quantization condition.","url_abs":"https://arxiv.org/abs/2305.09171v1","url_pdf":"https://arxiv.org/pdf/2305.09171v1.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":"wilson-loops-holomorphic-anomaly-equations","repo_url":"https://github.com/wangxin07895123/wilsonloop5d","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}