论文标题
顶点操作员代数和Orbifold保形场理论的表示理论
Representation theory of vertex operator algebras and orbifold conformal field theory
论文作者
论文摘要
我们在程序中讨论了一些基本问题和猜想，以使用顶点操作员代数的表示理论来构建一般的Orbifold共同场理论。我们首先审查了一个构建共形领域理论的程序。我们还阐明了对顶点操作员代数，模块化函数和交织操作员代数的一些误解。然后，我们讨论了数学轨道共形场理论中一些基本的开放问题和猜想。审查了广义的扭曲模块及其变体，它们的构造和某些存在结果。还审查了扭曲的交织操作员及其基本属性。然后，在基本的开放问题和上述猜想中的猜想特性得到精确和明确的表达。还讨论了作者对Orbifold共形领域理论的进一步发展的一些想法。
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories. We also clarify some misunderstandings on vertex operator algebras, modular functors and intertwining operator algebras. Then we discuss some basic open problems and conjectures in mathematical orbifold conformal field theory. Generalized twisted modules and their variants, their constructions and some existence results are reviewed. Twisted intertwining operators and their basic properties are also reviewed. The conjectural properties in the basic open problems and conjectures mentioned above are then formulated precisely and explicitly. Some thoughts of the author on further developments of orbifold conformal field theory are also discussed.
