Conformal welding and the matter--Liouville--ghost factorisation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911031033331712 |
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| author | Baverez, Guillaume Jego, Antoine |
| author_facet | Baverez, Guillaume Jego, Antoine |
| contents | We study the action of local conformal transformations on several measures related to the Gaussian free field and Schramm--Loewner evolutions. The main novelty of our work is a Cameron--Martin-type formula for the welding homeomorphism of the SLE loop measure ($κ\in(0,4]$); its proof relies on a rigorous interpretation (and computation) of the "Jacobian" of the conformal welding map, which we relate to the "$bc$-ghost system" from bosonic string theory. We also give an intrinsic definition of the trace of the GFF on SLE, and prove a characterisation of the free boundary GFF in $\mathbb{D}$. As an application, we introduce a new and intrinsic approach to the conformal welding of quantum surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal welding and the matter--Liouville--ghost factorisation Baverez, Guillaume Jego, Antoine Probability Mathematical Physics Complex Variables Representation Theory Primary: 60J67, 60G60, 17B68. Secondary: 81T40, 30C62 We study the action of local conformal transformations on several measures related to the Gaussian free field and Schramm--Loewner evolutions. The main novelty of our work is a Cameron--Martin-type formula for the welding homeomorphism of the SLE loop measure ($κ\in(0,4]$); its proof relies on a rigorous interpretation (and computation) of the "Jacobian" of the conformal welding map, which we relate to the "$bc$-ghost system" from bosonic string theory. We also give an intrinsic definition of the trace of the GFF on SLE, and prove a characterisation of the free boundary GFF in $\mathbb{D}$. As an application, we introduce a new and intrinsic approach to the conformal welding of quantum surfaces. |
| title | Conformal welding and the matter--Liouville--ghost factorisation |
| topic | Probability Mathematical Physics Complex Variables Representation Theory Primary: 60J67, 60G60, 17B68. Secondary: 81T40, 30C62 |
| url | https://arxiv.org/abs/2502.17076 |