标题： 非半单共形场论中一致的关联函数系统 显示英文标题

标题： Consistent systems of correlators in non-semisimple conformal field theory

摘要： 基于与一个非退化 ribbon 范畴$\mathcal D$（不一定半单）相关的模函子，我们给出了共形场论中一致的体场相关函数系统的定义，该系统包括在映射类群作用下的不变性以及曲面缝合的相容性。 我们证明了当限制到亏格为零的曲面时，这类系统与$\mathcal D$中的交换对称 Frobenius 代数一一对应；而对于任意亏格的曲面，它们与$\mathcal D$中的模 Frobenius 代数一一对应。 这为从理性共形场论中熟悉的一些结构提供了新的见解，并将其扩展到了刚性对数共形场论。 显示英文摘要

摘要： Based on the modular functor associated with a -- not necessarily semisimple -- finite non-degenerate ribbon category $\mathcal D$, we present a definition of a consistent system of bulk field correlators for a conformal field theory which comprises invariance under mapping class group actions and compatibility with the sewing of surfaces. We show that when restricting to surfaces of genus zero such systems are in bijection with commutative symmetric Frobenius algebras in $\mathcal D$, while for surfaces of any genus they are in bijection with modular Frobenius algebras in $\mathcal D$. This provides additional insight into structures familiar from rational conformal field theories and extends them to rigid logarithmic conformal field theories.