论文标题
边界的一致性liouville共形场理论
Integrability of boundary Liouville conformal field theory
论文作者
论文摘要
在与边界的简单连接域上考虑了liouville共形田地理论（LCFT），专门针对liouville电位仅在域边界上集成的情况。我们在Huang-Rhodes-Vargas（2015）引入的边界LCFT的概率框架中工作。基于第一作者的批量单点函数的已知证明，精确的公式是为理论的其余基本相关函数（即散装边界相关器，边界的两点和边界三点函数）严格得出的。这四个相关性应被视为边界理论的基本构建基础，在Riemann Sphere的情况下扮演了Dozz公式的模拟角色。我们对边界LCFT的研究还提供了一般框架，以了解一维高斯混乱措施及其尾部扩展的整合性。最终，这些结果在研究CFT的保形块中有应用，并为更一般的边界LCFT案例奠定了基础，并具有散装和边界的Liouville电位。
Liouville conformal field theory (LCFT) is considered on a simply connected domain with boundary, specializing to the case where the Liouville potential is integrated only over the boundary of the domain. We work in the probabilistic framework of boundary LCFT introduced by Huang-Rhodes-Vargas (2015). Building upon the known proof of the bulk one-point function by the first author, exact formulas are rigorously derived for the remaining basic correlation functions of the theory, i.e., the bulk-boundary correlator, the boundary two-point and the boundary three-point functions. These four correlations should be seen as the fundamental building blocks of boundary Liouville theory, playing the analogue role of the DOZZ formula in the case of the Riemann sphere. Our study of boundary LCFT also provides the general framework to understand the integrability of one-dimensional Gaussian multiplicative chaos measures as well as their tail expansions. Finally these results have applications to studying the conformal blocks of CFT and set the stage for the more general case of boundary LCFT with both bulk and boundary Liouville potentials.
