Conformal fields, restriction properties, degenerate representations and SLE

Roland Friedrich; Wendelin Werner

doi:10.1016/S1631-073X(02)02581-5

Conformal fields, restriction properties, degenerate representations and SLE
[Champs conformes, propriété de restriction, représentations dégénérées et SLE]

Roland Friedrich ¹ ; Wendelin Werner ¹

¹ Laboratoire de mathématiques, Université Paris-Sud, 91405 Orsay cedex, France

Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 947-952.

Résumé
Abstract

Nous relions le processus de Schramm–Loewner (SLE) à certaines représentations de plus haut poids dégénérées de l'algèbre de Virasoro. Les propriétés de restriction du SLE étudiées dans [19] s'avèrent être importantes pour établir ce lien. Par ailleurs, diverses considérations et relations de la théorie conforme des champs peuvent ainsi être interprétées en termes du SLE. Ceci permet de faire le lien entre les modèles issus de la physique statistique et la théorie conforme des champs.

We relate the Schramm–Loewner Evolution processes (SLE) to highest-weight representations of the Virasoro Algebra. The restriction properties of SLE that have been recently derived in [19] play a crucial role. In this setup, various considerations from conformal field theory can be interpreted and reformulated via SLE. This enables one to make a concrete link between the two-dimensional discrete critical systems from statistical physics and conformal field theory.

Reçu le : 2002-09-28
Accepté le : 2002-10-04
Publié le : 2002-10-29

DOI : 10.1016/S1631-073X(02)02581-5

Affiliations des auteurs :

Roland Friedrich ¹ ; Wendelin Werner ¹

¹ Laboratoire de mathématiques, Université Paris-Sud, 91405 Orsay cedex, France

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Roland Friedrich; Wendelin Werner. Conformal fields, restriction properties, degenerate representations and SLE. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 947-952. doi : 10.1016/S1631-073X(02)02581-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02581-5/

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