# Conformal field theory on the plane

Abstract : We provide an introduction to conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. We describe the mathematical structures which appear in such theories, from the Virasoro algebra and its representations, to the BPZ equations and their solutions. As examples, we study a number of models: Liouville theory, (generalized) minimal models, free bosonic theories, the $H_3^+$ model, and the $SU_2$ and $\widetilde{SL}_2(\mathbb{R})$ WZW models.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-cea.archives-ouvertes.fr/cea-01062770
Contributor : Emmanuelle de Laborderie <>
Submitted on : Wednesday, September 10, 2014 - 3:07:11 PM
Last modification on : Monday, February 10, 2020 - 6:13:39 PM

### Identifiers

• HAL Id : cea-01062770, version 1
• ARXIV : 1406.4290

### Citation

Sylvain Ribault. Conformal field theory on the plane. 2014. ⟨cea-01062770⟩

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