Boundary operators in the Brownian loop soup
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908749690568704 |
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| author | Camia, Federico Nivesvivat, Rongvoram |
| author_facet | Camia, Federico Nivesvivat, Rongvoram |
| contents | We obtain infinitely many boundary operators in the Brownian loop soup in the subcritical phase by analyzing the conformal block expansion of the two-point function that computes the probability of having two marked points on the upper half-plane being separated by Brownian loops. The resulting boundary operators are primary operators in a 2D CFT with central charge $c\leq1$ and have conformal dimensions that are non-negative integers. By comparing the above-mentioned conformal block expansion with probabilities in the Brownian loop soup, we provide a physical interpretation of the boundary operators of even dimensions as operators that insert multiple outer boundaries of Brownian loops at points on the real axis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02755 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundary operators in the Brownian loop soup Camia, Federico Nivesvivat, Rongvoram Mathematical Physics Statistical Mechanics High Energy Physics - Theory Probability We obtain infinitely many boundary operators in the Brownian loop soup in the subcritical phase by analyzing the conformal block expansion of the two-point function that computes the probability of having two marked points on the upper half-plane being separated by Brownian loops. The resulting boundary operators are primary operators in a 2D CFT with central charge $c\leq1$ and have conformal dimensions that are non-negative integers. By comparing the above-mentioned conformal block expansion with probabilities in the Brownian loop soup, we provide a physical interpretation of the boundary operators of even dimensions as operators that insert multiple outer boundaries of Brownian loops at points on the real axis. |
| title | Boundary operators in the Brownian loop soup |
| topic | Mathematical Physics Statistical Mechanics High Energy Physics - Theory Probability |
| url | https://arxiv.org/abs/2601.02755 |