Comptes Rendus
no. 6
A probabilistic approach of Liouville field theory
[Une approche probabiliste de la théorie des champs de Liouville]
Rémi Rhodes1, 2  ; Vincent Vargas3
1 Aix-Marseille University (AMU), Institut de Mathématiques (I2M), 39 rue F. Joliot Curie, Marseille, France.
2 Institut Universitaire de France (IUF)
3 Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, Villetaneuse, France
Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 561-569.

Dans cet article, nous présentons la théorie des champs de Liouville, qui fut introduite en physique dans les années 80 par Polyakov comme modèle de métriques aléatoires dans le cadre de la gravité quantique 2D, et donnons un aperçu de la construction probabiliste de cette théorie proposée par David–Kupiainen–Rhodes–Vargas dans []. Nous expliquons comment cette construction se relie à l’approche moderne des théories conformes de champs en physique appelée conformal bootstrap et basée sur la théorie des représentations.

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.

Publié le :
DOI : 10.5802/crphys.43
Classification : 60D05, 81T40, 81T20
Mots clés : $2D$ quantum gravity, path integral, Liouville field theory, conformal bootstrap
Rémi Rhodes 1, 2 ; Vincent Vargas 3

1 Aix-Marseille University (AMU), Institut de Mathématiques (I2M), 39 rue F. Joliot Curie, Marseille, France.
2 Institut Universitaire de France (IUF)
3 Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, Villetaneuse, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A probabilistic approach of {Liouville} field theory},
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     pages = {561--569},
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Rémi Rhodes; Vincent Vargas. A probabilistic approach of Liouville field theory. Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 561-569. doi : 10.5802/crphys.43. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.43/

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