Exact solution of three-point functions in critical loop models
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914451265945600 |
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| author | Ang, Morris Cai, Gefei Jacobsen, Jesper Lykke Nivesvivat, Rongvoram Roux, Paul Sun, Xin Wu, Baojun |
| author_facet | Ang, Morris Cai, Gefei Jacobsen, Jesper Lykke Nivesvivat, Rongvoram Roux, Paul Sun, Xin Wu, Baojun |
| contents | We propose an exact formula for three-point functions on the sphere in critical loop models with primary fields $V_{(r,s)}$ characterized by $2r$ legs and a parameter \(s\) that describes diagonal fields for $r=0$ and the momentum of legs for $r>0$. We demonstrate its validity in three ways: the conformal bootstrap method for 4-point functions, a transfer-matrix study of the lattice model, and a probabilistic method based on conformal loop ensemble and Liouville quantum gravity. This work provides a crucial missing piece for solving critical loop models and reveals a deep unity between three fundamental approaches to 2D statistical physics: transfer matrix, conformal field theory, and probability theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05503 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact solution of three-point functions in critical loop models Ang, Morris Cai, Gefei Jacobsen, Jesper Lykke Nivesvivat, Rongvoram Roux, Paul Sun, Xin Wu, Baojun Statistical Mechanics Mathematical Physics Probability We propose an exact formula for three-point functions on the sphere in critical loop models with primary fields $V_{(r,s)}$ characterized by $2r$ legs and a parameter \(s\) that describes diagonal fields for $r=0$ and the momentum of legs for $r>0$. We demonstrate its validity in three ways: the conformal bootstrap method for 4-point functions, a transfer-matrix study of the lattice model, and a probabilistic method based on conformal loop ensemble and Liouville quantum gravity. This work provides a crucial missing piece for solving critical loop models and reveals a deep unity between three fundamental approaches to 2D statistical physics: transfer matrix, conformal field theory, and probability theory. |
| title | Exact solution of three-point functions in critical loop models |
| topic | Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2604.05503 |