Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap

[2607.18375] Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap Skip to main content Search Submit Donate Log in High Energy Physics - Theory arXiv:2607.18375 (hep-th) [Submitted on 20 Jul 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap Authors: Arpit Das , Sunil Mukhi View PDF HTML (experimental) Abstract: Characters of rational conformal field theories solve modular linear differential equations labelled by their order and the Wronskian index $\ell$. Direct classification of admissible solutions by solving MLDEs becomes increasingly difficult at higher $\ell$ -- where movable poles and accessory parameters appear. In this work we introduce differential operators that relate higher-$\ell$ solutions to lower-$\ell$ ones while preserving modular covariance and integrality of the \(q\)-series. In rank two, this generates all allowed Wronskian sectors from the Mathur--Mukhi--Sen equation. In rank three and higher, it reduces the construction of higher-$\ell$ quasi-characters to simpler equations with lower $\ell$. This gives an efficient new route for organising candidate RCFT characters, and more generally quasi-characters, across the Wronskian tower. As an application, we apply our construction to prove a previously conjectured property on the signs of $\ell=2$ quasi-characters in rank 2. Comments: 47 pages (including references). v2: minor changes to appendices and main text, typos corrected, main results unchanged Subjects: High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph); Number Theory (math.NT); Quantum Algebra (math.QA); Representation Theory (math.RT) Cite as: arXiv:2607.18375 [hep-th] (or arXiv:2607.18375v2 [hep-th] for this version) https://doi.org/10.48550/arXiv.2607.18375 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arpit Das [ view email ] [v1] Mon, 20 Jul 2026 18:00:00 UTC (82 KB) [v2] Tue, 25 Aug 2026 09:01:25 UTC (67 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-07 Change to browse by: math math-ph math.MP math.NT math.QA math.RT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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