论文标题
共形场理论中的融合
Convergence in conformal field theory
论文作者
论文摘要
收敛和分析扩展在数学结构和保形场理论研究中至关重要。我们使用顶点操作员代数的表示理论回顾了一些主要的融合结果，猜想和构建和研究的问题。我们还回顾了相关的分析扩展结果，猜想和问题。我们讨论了交织运营商（手性的保形场）以及$ q $ trace和pseudo- $ q $ - 相互交织运营商的产品的融合和分析扩展。我们还讨论了与缝纫操作以及行列式线束和更高的收敛结果有关的收敛结果。然后，我们解释了Orbifold共形场理论和顶点操作员代数的共同体学理论中有关收敛和分析扩展的猜想和问题。
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.
