En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK
1

Conformal bootstrap in Liouville theory

Sélection Signaler une erreur
Multi angle
Auteurs : Vargas, Vincent (Auteur de la conférence)
CIRM (Editeur )

Loading the player...

Résumé : Liouville conformal field theory (LCFT) was introduced by Polyakov in 1981 as an essential ingredient in his path integral construction of string theory. Since then Liouville theory has appeared in a wide variety of contexts ranging from random conformal geometry to 4d Yang-Mills theory with supersymmetry.
Recently, a probabilistic construction of LCFT on general Riemann surfaces was provided using the 2d Gaussian Free Field. This construction can be seen as a rigorous construction of the 2d path integral introduced in Polyakov's 1981 work. In contrast to this construction, modern conformal field theory is based on representation theory and the so-called bootstrap procedure (based on recursive techniques) introduced in 1984 by Belavin-Polyakov-Zamolodchikov. In particular, a bootstrap construction for LCFT has been proposed in the mid 90's by Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ) on the sphere. The aim of this talk is to review a recent series of work which shows the equivalence between the probabilistic construction and the bootstrap construction of LCFT on general Riemann surfaces. In particular, the equivalence is based on showing that LCFT satisfies a set of natural geometric axioms known as Segal's axioms.
Based on joint works with F. David, C. Guillarmou, A. Kupiainen, R. Rhodes.

Codes MSC :
60D99 - Geometric probability and stochastic geometry
17B68 - Virasoro and related algebras
37K15 - Integration of completely integrable systems by inverse spectral and scattering methods
81T40 - Two-dimensional field theories, conformal field theories, etc.
81U20 - $S$-matrix theory, etc.
47D08 - Schrödinger and Feynman-Kac semigroups

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de Publication : 04/02/2022
    Date de Captation : 20/01/2022
    Sous Collection : Research talks
    Catégorie arXiv : Probability ; Mathematical Physics ; Representation Theory ; Spectral Theory
    Format : MP4 (.mp4) - HD
    Durée : 00:51:37
    Audience : Chercheurs
    Download : https://videos.cirm-math.fr/2022-01-20_Vargas.mp4

Informations sur la Rencontre

Nom de la Rencontre : Random Geometry / Géométrie aléatoire
Organisateurs de la Rencontre : Curien, Nicolas ; Goldschmidt, Christina ; Le Gall, Jean-François ; Miermont, Grégory ; Rhodes, Rémi
Dates : 17/01/2022 - 21/01/2022
Année de la rencontre : 2022
URL de la Rencontre : https://conferences.cirm-math.fr/2528.html

Données de citation

DOI : 10.24350/CIRM.V.19877803
Citer cette vidéo: Vargas, Vincent (2022). Conformal bootstrap in Liouville theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19877803
URI : http://dx.doi.org/10.24350/CIRM.V.19877803

Voir Aussi

Bibliographie



Imagette Video

Sélection Signaler une erreur