Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915023975088128 |
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| author | Gordina, Maria Qian, Wei Wang, Yilin |
| author_facet | Gordina, Maria Qian, Wei Wang, Yilin |
| contents | We use the SLE$_κ$ loop measure to construct a natural representation of the Virasoro algebra of central charge $c = c(κ) \le 1$. In particular, we introduce a non-degenerate bilinear Hermitian form (and non positive-definite) using the SLE loop measure and show that the representation is indefinite unitary. Our proof relies on the infinitesimal conformal restriction property of the SLE loop measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra Gordina, Maria Qian, Wei Wang, Yilin Probability Mathematical Physics 60J67, 30C55, 58J65 We use the SLE$_κ$ loop measure to construct a natural representation of the Virasoro algebra of central charge $c = c(κ) \le 1$. In particular, we introduce a non-degenerate bilinear Hermitian form (and non positive-definite) using the SLE loop measure and show that the representation is indefinite unitary. Our proof relies on the infinitesimal conformal restriction property of the SLE loop measure. |
| title | Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra |
| topic | Probability Mathematical Physics 60J67, 30C55, 58J65 |
| url | https://arxiv.org/abs/2407.09426 |