Lecture notes on Liouville theory and the DOZZ formula

Abstract

The purpose of these notes, based on a series of 4 lectures given by the author at IHES, is to explain the recent proof of the DOZZ formula for the three point correlation functions of Liouville conformal field theory (LCFT). We first review the probabilistic construction of the $N$ point correlation functions of LCFT on the Riemann sphere for $N\ge 3$ (based on a series of works of the author with David, Kupiainen and Rhodes). We then explain the construction of the two point correlation functions of LCFT, also called reflection coefficient. These probabilistic constructions will be justified from the point of view of Polyakov's path integral formulation of LCFT. Finally, we explain the proof of the DOZZ formula for the three point correlation functions of LCFT (based on 2 papers by the author with Kupiainen and Rhodes).

arXiv comment30 pages

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Cited by in corpus (10)

• Mating of trees for random planar maps and Liouville quantum gravity: a survey
• A slow review of the AGT correspondence
• Lecture notes on the Gaussian Free Field
• Integrability of Liouville theory: proof of the DOZZ Formula
• The distribution of Gaussian multiplicative chaos on the unit interval
• Path integral approach to analytic continuation of Liouville theory: the pencil region
• Tensor Field Theories: Renormalization and Random Geometry
• Introduction to the Liouville quantum gravity metric
• Higher order BPZ equations for Liouville conformal field theory
• A Family of Probability Distributions Consistent with the DOZZ Formula: Towards a Conjecture for the Law of 2D GMC