Auteurs : Guillarmou, Colin (Auteur de la conférence)
CIRM (Editeur )
Résumé :
Liouville CFT is a conformal field theory developped in the early 80s in physics, it describes random surfaces and more precisely random Riemannian metrics on surfaces. We will explain, using the Gaussian multiplicative chaos, how to associate to each surface $\Sigma$ with boundary an amplitude, which is an $L^2$ function on the space of fields on the boundary of $\Sigma$ (i.e. the Sobolev space $H^{-s}(\mathbb{S}^1)^b$ equipped with a Gaussian measure, if the boundary of $\Sigma$ has $b$ connected components), and then how these amplitudes compose under gluing of surfaces along their boundary (the so-called Segal axioms).
This allows us to give formulas for all partition and correlation functions of the Liouville CFT in terms of $3$ point correlation functions on the Riemann sphere (DOZZ formula) and the conformal blocks, which are holomorphic functions of the moduli of the space of Riemann surfaces with marked points. This gives a link between the probabilistic approach and the representation theory approach for CFTs, and a mathematical construction and resolution of an important non-rational conformal field theory.
This is joint work with A. Kupiainen, R. Rhodes and V. Vargas.
Mots-Clés : conformal field theory; Gaussian multiplicative chaos; conformal blocks
Codes MSC :
17B68
- Virasoro and related algebras
17B69
- Vertex operators; vertex operator algebras and related structures
60D05
- Geometric probability and stochastic geometry
81R10
- Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W-algebras and other current algebras and their representations
81T80
- Simulation and numerical modeling
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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
DOI : 10.24350/CIRM.V.19878003
Citer cette vidéo:
Guillarmou, Colin (2022). Resolution of Liouville CFT : Segal axioms and bootstrap. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19878003
URI : http://dx.doi.org/10.24350/CIRM.V.19878003
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Bibliographie
- GUILLARMOU, Colin, KUPIAINEN, Antti, RHODES, Rémi, et al. Segal's axioms and bootstrap for Liouville Theory. arXiv preprint arXiv:2112.14859, 2021. - https://arxiv.org/abs/2112.14859
- GUILLARMOU, Colin, KUPIAINEN, Antti, RHODES, Rémi, et al. Conformal bootstrap in Liouville Theory. arXiv preprint arXiv:2005.11530, 2020. - https://arxiv.org/abs/2005.11530