Conformal welding of quantum disks and multiple SLE: the non-simple case
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917016253759488 |
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| author | Ang, Morris Holden, Nina Sun, Xin Yu, Pu |
| author_facet | Ang, Morris Holden, Nina Sun, Xin Yu, Pu |
| contents | Two-pointed quantum disks with a weight parameter $W>0$ is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We extend the conformal welding of quantum disks in [AHS23] to the non-simple regime, and give a construction of the multiple SLE associated with any given link pattern for $κ\in(4,8)$. Our proof is based on connections between SLE and Liouville conformal field theory (LCFT), where we show that in the conformal welding of multiple forested quantum disks, the surface after welding can be described in terms of LCFT, and the random conformal moduli contains the SLE partition function for the interfaces as a multiplicative factor. As a corollary, for $κ\in(4,8)$, we prove the existence of the multiple SLE partition functions, which are smooth functions satisfying a system of PDEs and conformal covariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20583 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformal welding of quantum disks and multiple SLE: the non-simple case Ang, Morris Holden, Nina Sun, Xin Yu, Pu Probability Mathematical Physics 60J67, 60G60 Two-pointed quantum disks with a weight parameter $W>0$ is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We extend the conformal welding of quantum disks in [AHS23] to the non-simple regime, and give a construction of the multiple SLE associated with any given link pattern for $κ\in(4,8)$. Our proof is based on connections between SLE and Liouville conformal field theory (LCFT), where we show that in the conformal welding of multiple forested quantum disks, the surface after welding can be described in terms of LCFT, and the random conformal moduli contains the SLE partition function for the interfaces as a multiplicative factor. As a corollary, for $κ\in(4,8)$, we prove the existence of the multiple SLE partition functions, which are smooth functions satisfying a system of PDEs and conformal covariance. |
| title | Conformal welding of quantum disks and multiple SLE: the non-simple case |
| topic | Probability Mathematical Physics 60J67, 60G60 |
| url | https://arxiv.org/abs/2310.20583 |