2017/12/03 by Vincent Vargas, Vargas, Vincent · 2 citations
Mathematics · Physics and Astronomy · #60D05 #81T20 #81T40 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1712.00829
openalex publication_date 2017/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≥ 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).