A probabilistic approach of Liouville field theory
In this article, we present the Liouville field theory, which was introduced in the eighties in physics by Polyakov as a model for fluctuating metrics in 2D quantum gravity, and outline recent mathematical progress in its study. In particular, we explain the probabilistic construction of this theory...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-01-01
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| Series: | Comptes Rendus. Physique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.43/ |
| _version_ | 1797651397397708800 |
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| author | Rhodes, Rémi Vargas, Vincent |
| author_facet | Rhodes, Rémi Vargas, Vincent |
| author_sort | Rhodes, Rémi |
| collection | DOAJ |
| description | In this article, we present the Liouville field theory, which was introduced in the eighties in physics by Polyakov as a model for fluctuating metrics in 2D quantum gravity, and outline recent mathematical progress in its study. In particular, we explain the probabilistic construction of this theory carried out by David–Kupiainen–Rhodes–Vargas in [] and how this construction connects to the modern and general approach of Conformal Field Theories in physics, called conformal bootstrap and based on representation theory. |
| first_indexed | 2024-03-11T16:15:21Z |
| format | Article |
| id | doaj.art-9a910d7449d048d88c1330f8b0a8e06a |
| institution | Directory Open Access Journal |
| issn | 1878-1535 |
| language | English |
| last_indexed | 2024-03-11T16:15:21Z |
| publishDate | 2021-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Physique |
| spelling | doaj.art-9a910d7449d048d88c1330f8b0a8e06a2023-10-24T14:21:48ZengAcadémie des sciencesComptes Rendus. Physique1878-15352021-01-0121656156910.5802/crphys.4310.5802/crphys.43A probabilistic approach of Liouville field theoryRhodes, Rémi0Vargas, Vincent1Aix-Marseille University (AMU), Institut de Mathématiques (I2M), 39 rue F. Joliot Curie, Marseille, France.; Institut Universitaire de France (IUF)Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, Villetaneuse, FranceIn this article, we present the Liouville field theory, which was introduced in the eighties in physics by Polyakov as a model for fluctuating metrics in 2D quantum gravity, and outline recent mathematical progress in its study. In particular, we explain the probabilistic construction of this theory carried out by David–Kupiainen–Rhodes–Vargas in [] and how this construction connects to the modern and general approach of Conformal Field Theories in physics, called conformal bootstrap and based on representation theory.https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.43/$2D$ quantum gravitypath integralLiouville field theoryconformal bootstrap |
| spellingShingle | Rhodes, Rémi Vargas, Vincent A probabilistic approach of Liouville field theory Comptes Rendus. Physique $2D$ quantum gravity path integral Liouville field theory conformal bootstrap |
| title | A probabilistic approach of Liouville field theory |
| title_full | A probabilistic approach of Liouville field theory |
| title_fullStr | A probabilistic approach of Liouville field theory |
| title_full_unstemmed | A probabilistic approach of Liouville field theory |
| title_short | A probabilistic approach of Liouville field theory |
| title_sort | probabilistic approach of liouville field theory |
| topic | $2D$ quantum gravity path integral Liouville field theory conformal bootstrap |
| url | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.43/ |
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