Conformal field theory of Gaussian free fields in a multiply connected domain
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916319977275392 |
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| author | Alberts, Tom Byun, Sung-Soo Kang, Nam-Gyu |
| author_facet | Alberts, Tom Byun, Sung-Soo Kang, Nam-Gyu |
| contents | We implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is based on the Gaussian free field and applies to CFTs with central charge $c \leq 1$. In this framework we introduce the generalized Eguchi-Ooguri equations and use them to derive the explicit form of Ward's equations, which describe the insertion of a stress tensor in terms of Lie derivatives and differential operators depending on the Teicmüller modular parameters. Furthermore, by implementing the BPZ equations, we provide a conformal field theoretic realization of an SLE in a multiply connected domain, which in particular suggests its drift function, and construct a class of martingale observables for this SLE process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal field theory of Gaussian free fields in a multiply connected domain Alberts, Tom Byun, Sung-Soo Kang, Nam-Gyu Mathematical Physics Complex Variables Probability We implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is based on the Gaussian free field and applies to CFTs with central charge $c \leq 1$. In this framework we introduce the generalized Eguchi-Ooguri equations and use them to derive the explicit form of Ward's equations, which describe the insertion of a stress tensor in terms of Lie derivatives and differential operators depending on the Teicmüller modular parameters. Furthermore, by implementing the BPZ equations, we provide a conformal field theoretic realization of an SLE in a multiply connected domain, which in particular suggests its drift function, and construct a class of martingale observables for this SLE process. |
| title | Conformal field theory of Gaussian free fields in a multiply connected domain |
| topic | Mathematical Physics Complex Variables Probability |
| url | https://arxiv.org/abs/2407.08220 |