论文标题
通过关键模块类别的有限CFT边界的散装
Bulk from boundary in finite CFT by means of pivotal module categories
论文作者
论文摘要
我们提出了明确的数学结构，从其边界场中重建了完整的局部保形场理论的字段内容。我们的框架是模块化张量类别之一，而无需半透明性，因此涵盖了特别有限的刚性刚性对数磁场理论。我们假设边界数据由模块化张量类别的关键模块类别描述，这确保边界场的代数为Frobenius代数。插入缺陷线上的散装字段以及插入在缺陷线上的缺陷场是由标记缺陷线类型的函数之间的内部自然变换给出的。我们使用内部自然变换理论来识别缺陷场的操作员产品的候选者（其中有两种类型，沿单个缺陷线，或伴随着两条缺陷线的融合），以及散装型op。我们表明，所获得的OPES通过了各种一致性条件，包括Lewellen列表中的所有零属约束。
We present explicit mathematical structures that allow for the reconstruction of the field content of a full local conformal field theory from its boundary fields. Our framework is the one of modular tensor categories, without requiring semisimplicity, and thus covers in particular finite rigid logarithmic conformal field theories. We assume that the boundary data are described by a pivotal module category over the modular tensor category, which ensures that the algebras of boundary fields are Frobenius algebras. Bulk fields and, more generally, defect fields inserted on defect lines, are given by internal natural transformations between the functors that label the types of defect lines. We use the theory of internal natural transformations to identify candidates for operator products of defect fields (of which there are two types, either along a single defect line, or accompanied by the fusion of two defect lines), and for bulk-boundary OPEs. We show that the so obtained OPEs pass various consistency conditions, including in particular all genus-zero constraints in Lewellen's list.
