共形域论的收敛性
Convergence in conformal field theory
摘要：
收敛性和解析延拓是共形域论的数学构造和研究中的重要问题。本文综述了利用顶点算子代数的表示论构造和研究共形域论中的一些主要收敛性结果、结构和问题。我们也回顾了相关的解析延拓结果、定理和问题。本文讨论了缠绕算子（手征共形场）的乘积和缠绕算子的乘积的$q$ -迹和伪$q$ -迹的收敛性和解析扩张.我们还讨论了与缝纫操作和行列式线丛有关的收敛结果和一个更高亏格的收敛结果。然后，我们解释了在轨道共形域论和顶点算子代数的上同调理论中的收敛性和解析扩张问题。
英文摘要：
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. We review some main convergence results, conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras. We also review the related analytic extension results, conjectures and problems. We discuss the convergence and analytic extensions of products of intertwining operators (chiral conformal fields) and of $q$-traces and pseudo-$q$-traces of products of intertwining operators. We also discuss the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result. We then explain conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.
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