A probabilistic approach of Liouville field theory

Rémi Rhodes; Vincent Vargas

doi:10.5802/crphys.43

A probabilistic approach of Liouville field theory

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

Comptes Rendus. Physique, Prizes of the French Academy of Sciences 2019 (continued), Volume 21 (2020) no. 6, pp. 561-569.

Abstract
Résumé

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.

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.

Published online: 2021-01-14

DOI: 10.5802/crphys.43

Classification: 60D05, 81T40, 81T20
Mots-clés : $2D$ quantum gravity, path integral, Liouville field theory, conformal bootstrap

Author's affiliations:

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@article{CRPHYS_2020__21_6_561_0,
     author = {R\'emi Rhodes and Vincent Vargas},
     title = {A probabilistic approach of {Liouville} field theory},
     journal = {Comptes Rendus. Physique},
     pages = {561--569},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {21},
     number = {6},
     year = {2020},
     doi = {10.5802/crphys.43},
     language = {en},
}

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Rémi Rhodes; Vincent Vargas. A probabilistic approach of Liouville field theory. Comptes Rendus. Physique, Prizes of the French Academy of Sciences 2019 (continued), 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/

References
Cited by

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