论文标题
liouville cft的概率保形块
Probabilistic conformal blocks for Liouville CFT on the torus
论文作者
论文摘要
Virasoro共形块是通过Virasoro代数定义为功率序列的重要功能的家族。它们是2D共形场理论（CFT）的共形性自举程序的基本输入，并且通过Alday-Gaiotto-Tachikawa对应关系与四个维度超对称量表理论密切相关。本工作为中央变化大于25的1分曲奇Virasoro保形块提供了概率的结构。更确切地说，我们使用称为高斯多种多重混乱（GMC）的概率工具构建了一个分析函数，并证明其功率系列膨胀与1点折磨Virasoro conformo块相一致。中央费用的范围$（25，\ infty）$对应于liouville CFT，这是一个重要的CFT，源自2D量子重力和玻色丝理论。我们的工作揭示了GMC的一个新的可集成结构，并为研究Virasoro共形块的非扰动性质（例如它们的分析延续和模块化对称性）打开了大门。我们的证明将对GMC的分析与CFT的工具相结合，例如Belavin-Polyakov-Zamolodchikov微分方程，运营商产品扩展和Dotsenko-Fateev型积分。
Virasoro conformal blocks are a family of important functions defined as power series via the Virasoro algebra. They are a fundamental input to the conformal bootstrap program for 2D conformal field theory (CFT) and are closely related to four dimensional supersymmetric gauge theory through the Alday-Gaiotto-Tachikawa correspondence. The present work provides a probabilistic construction of the 1-point toric Virasoro conformal block for central change greater than 25. More precisely, we construct an analytic function using a probabilistic tool called Gaussian multiplicative chaos (GMC) and prove that its power series expansion coincides with the 1-point toric Virasoro conformal block. The range $(25,\infty)$ of central charges corresponds to Liouville CFT, an important CFT originating from 2D quantum gravity and bosonic string theory. Our work reveals a new integrable structure underlying GMC and opens the door to the study of non-perturbative properties of Virasoro conformal blocks such as their analytic continuation and modular symmetry. Our proof combines an analysis of GMC with tools from CFT such as Belavin-Polyakov-Zamolodchikov differential equations, operator product expansions, and Dotsenko-Fateev type integrals.
