发表机构
Beijing International Center for Mathematical Research, Peking University; Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay; University of Helsinki, Department of Mathematics and Statistics; Aix-Marseille University, Institut de Mathématiques de Marseille (I2M), and Institut Universitaire de France (IUF)（北京大学北京国际数学研究中心; 巴黎萨克雷大学，法国国家科学研究中心，奥赛数学实验室; 赫尔辛基大学数学与统计系; 艾克斯-马赛大学，马赛数学研究所（I2M），法国大学研究院（IUF））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从Liouville CFT构造了亏格g、m个标记点黎曼曲面上Virasoro共形块的全局全纯截面，满足Ward恒等式，并证明其承载映射类群的射影酉表示，对Moore-Seiberg移动有酉同构。
AI 中文摘要
在本文中，我们给出了当中心荷 $c>25$ 时，黎曼曲面（亏格为 $g$，具有 $m$ 个标记点）的 Teichmüller 空间上 Virasoro 共形块的全局构造。我们证明了它们是全纯线丛的全局全纯截面，并且满足 Ward 恒等式，该恒等式编码了它们的共形不变性。对于具有 3 个点的球面，共形块的空间是一维的。对于给定的标记黎曼曲面和标记的裤子分解，它通常是一个无穷维 Hilbert 空间，同构于 $L^2(\R_+^{3g-3+m})$，其中涉及 DOZZ 结构常数。我们证明它承载了映射类群的射影酉表示。更一般地，对于每个 Moore-Seiberg 移动，存在酉同构，将一个标记的裤子分解变为另一个。
英文摘要
In this article, we give a global construction of the Virasoro conformal blocks on Teichmüller space of Riemann surfaces of genus $g$ with $m$ marked points, when the central charge is $c>25$. We prove that they are global holomorphic sections of a holomorphic line bundle and they satisfy the Ward identity, which encodes their conformal invariance. For the sphere with $3$ points, the space of conformal blocks is one-dimensional. For a given marked Riemann surface and a marked pair of pants decomposition, it is in general an infinite dimensional Hilbert space, isomorphic to $L^2(\R_+^{3g-3+m})$ with respect to some measure involving the DOZZ structure constants. We show that it carries a projective unitary representation of the mapping class group. More generally, there are unitary isomorphisms for each Moore-Seiberg move, changing a marked pair of pants decomposition into another one.
