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 $N \geq 3$ (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).
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.00829
 arXiv:
 arXiv:1712.00829
 Bibcode:
 2017arXiv171200829V
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 81T40;
 81T20;
 60D05
 EPrint:
 30 pages