用于关键双范畴的弦网模型
String-net models for pivotal bicategories
AI总结：
本文将弦网构造从球面融合范畴推广到关键双范畴，建立图形演算并证明刚性可分Frobenius函子诱导与映射类群及缝合相容的线性映射，为二维共形场论关联子提供新工具。
摘要：
我们发展了一种模函子的弦网构造，其代数输入是一个关键双范畴；这推广了基于球面融合范畴的标准构造。我们构造中的一个基本要素是关键双范畴的图形演算，我们将其表示为一个有色花冠状范畴。该演算向有向曲面的全局化给出了双范畴弦网空间作为余极限。我们证明，严格关键双范畴之间的每个刚性可分Frobenius函子都会在相应的双范畴弦网空间之间诱导线性映射，这些映射与映射类群作用及缝合相容。我们的结果受到二维共形场论中关联子描述的启发，并对其有应用。
英文摘要：
We develop a string-net construction of a modular functor whose algebraic input is a pivotal bicategory; this extends the standard construction based on a spherical fusion category. An essential ingredient in our construction is a graphical calculus for pivotal bicategories, which we express in terms of a category of colored corollas. The globalization of this calculus to oriented surfaces yields the bicategorical string-net spaces as colimits. We show that every rigid separable Frobenius functor between strictly pivotal bicategories induces linear maps between the corresponding bicategorical string-net spaces that are compatible with the mapping class group actions and with sewing. Our results are inspired by and have applications to the description of correlators in two-dimensional conformal field theories.
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