刘维理论和DOZZ公式讲义
Lecture notes on Liouville theory and the DOZZ formula
摘要：
这些笔记的目的，根据作者在IHES的4个系列讲座，是为了解释最近证明的DOZZ公式的三点相关函数的刘维共形域论（LCFT）。我们首先审查的概率构造的$N$点相关函数的LCFT的黎曼球面上的$N \geq 3$（基于一系列的作品，作者与大卫，Kupiainen和罗兹）。然后，我们解释的两个点的相关函数的LCFT，也称为反射系数的建设。这些概率的建设将是合理的，从波利亚科夫的路径积分制定LCFT的观点。最后，我们解释了三点相关函数的DOZZ公式的证明（基于作者与Kupiainen和Rhodes的两篇论文）。
英文摘要：
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).
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