Rigorous results for timelike Liouville field theory

[2504.02348] Rigorous results for timelike Liouville field theory Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2504.02348 (math) [Submitted on 3 Apr 2025 ( v1 ), last revised 11 Apr 2026 (this version, v5)] Title: Rigorous results for timelike Liouville field theory Authors: Sourav Chatterjee View a PDF of the paper titled Rigorous results for timelike Liouville field theory, by Sourav Chatterjee View PDF HTML (experimental) Abstract: Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike Liouville field theory is a version of Liouville field theory where the kinetic term in the action appears with a negative sign, which makes it closer to a theory of quantum gravity than ordinary (spacelike) Liouville field theory. Making sense of this `wrong sign' requires a theory of Gaussian random variables with negative variance. Such a theory is developed in this paper, and is used to prove the timelike DOZZ formula for the $3$-point correlation function when the parameters satisfy the so-called `charge neutrality condition'. Expressions are derived also for the $k$-point correlation functions for all $k\ge 3$, and it is shown that these functions approach the correct semiclassical limits as the coupling constant is sent to zero Comments: 92 pages. Minor corrections in this revision. To appear in Forum of Math., Sigma Subjects: Probability (math.PR) ; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) MSC classes: 81T40, 17B69, 81T20 Cite as: arXiv:2504.02348 [math.PR] (or arXiv:2504.02348v5 [math.PR] for this version) https://doi.org/10.48550/arXiv.2504.02348 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Forum of Mathematics, Sigma 14 (2026) e71 Related DOI : https://doi.org/10.1017/fms.2026.10223 Focus to learn more DOI(s) linking to related resources Submission history From: Sourav Chatterjee [ view email ] [v1] Thu, 3 Apr 2025 07:33:00 UTC (63 KB) [v2] Mon, 7 Apr 2025 08:07:57 UTC (64 KB) [v3] Tue, 15 Apr 2025 14:56:05 UTC (65 KB) [v4] Wed, 7 Jan 2026 09:58:12 UTC (67 KB) [v5] Sat, 11 Apr 2026 17:51:31 UTC (68 KB) Full-text links: Access Paper: View a PDF of the paper titled Rigorous results for timelike Liouville field theory, by Sourav Chatterjee View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2025-04 Change to browse by: hep-th math math-ph math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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? ) 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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