The Virasoro structure and the scattering matrix for Liouville conformal field theory
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911953035722752 |
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| author | Baverez, Guillaume Guillarmou, Colin Kupiainen, Antti Rhodes, Rémi Vargas, Vincent |
| author_facet | Baverez, Guillaume Guillarmou, Colin Kupiainen, Antti Rhodes, Rémi Vargas, Vincent |
| contents | In this work, we construct a representation of the Virasoro algebra in the canonical Hilbert space associated to Liouville conformal field theory. The study of the Virasoro operators is performed through the introduction of a new family of Markovian dynamics associated to holomorphic vector fields defined in the disk. As an output, we show that the Hamiltonian of Liouville conformal field theory can be diagonalized through the action of the Virasoro algebra. This enables to show that the scattering matrix of the theory is diagonal and that the family of the so-called primary fields (which are eigenvectors of the Hamiltonian) admits an analytic extension to the whole complex plane, as conjectured in the physics literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02745 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Virasoro structure and the scattering matrix for Liouville conformal field theory Baverez, Guillaume Guillarmou, Colin Kupiainen, Antti Rhodes, Rémi Vargas, Vincent Probability Mathematical Physics Representation Theory Spectral Theory 60G60, 81T40 (Primary) 37K15, 81R10, 47D08 (Secondary) In this work, we construct a representation of the Virasoro algebra in the canonical Hilbert space associated to Liouville conformal field theory. The study of the Virasoro operators is performed through the introduction of a new family of Markovian dynamics associated to holomorphic vector fields defined in the disk. As an output, we show that the Hamiltonian of Liouville conformal field theory can be diagonalized through the action of the Virasoro algebra. This enables to show that the scattering matrix of the theory is diagonal and that the family of the so-called primary fields (which are eigenvectors of the Hamiltonian) admits an analytic extension to the whole complex plane, as conjectured in the physics literature. |
| title | The Virasoro structure and the scattering matrix for Liouville conformal field theory |
| topic | Probability Mathematical Physics Representation Theory Spectral Theory 60G60, 81T40 (Primary) 37K15, 81R10, 47D08 (Secondary) |
| url | https://arxiv.org/abs/2204.02745 |