作为扩展拓扑量子场论的截断仿射Rozansky--Witten模型
Truncated affine Rozansky--Witten models as extended TQFTs
AI总结：
本文从以T*C^n为目标的Rozansky–Witten模型出发，通过截断3-范畴得到体理论、面缺陷与线缺陷同构类的2-范畴，并应用配边假设构造唯一扩展定向2维TQFT，进而计算闭曲面态空间及圆周限制对应的交换Frobenius代数。
摘要：
我们构造了与目标流形为$T^*\mathbb{C}^n$的Rozansky--Witten模型相关的扩展拓扑量子场论（TQFT）。构造的起点是3-范畴，其对象为这类Rozansky--Witten模型，态射为所有余维数的缺陷。通过截断，我们得到体理论、表面缺陷和线缺陷同构类的（非半单）2-范畴$\mathcal{C}$。通过系统应用配边假设，我们为每个仿射Rozansky--Witten模型构造了唯一取值于$\mathcal{C}$的扩展定向2维TQFT。通过在闭曲面上计算该TQFT，我们得到初始3维理论的无穷维态空间（按味荷和R荷分级）。此外，我们显式计算了对扩展理论到圆周及其间配边的限制进行分类的交换Frobenius代数。
英文摘要：
We construct extended TQFTs associated to Rozansky--Witten models with target manifolds $T^*\mathbb{C}^n$. The starting point of the construction is the 3-category whose objects are such Rozansky--Witten models, and whose morphisms are defects of all codimensions. By truncation, we obtain a (non-semisimple) 2-category $\mathcal{C}$ of bulk theories, surface defects, and isomorphism classes of line defects. Through a systematic application of the cobordism hypothesis we construct a unique extended oriented 2-dimensional TQFT valued in $\mathcal{C}$ for every affine Rozansky--Witten model. By evaluating this TQFT on closed surfaces we obtain the infinite-dimensional state spaces (graded by flavour and R-charges) of the initial 3-dimensional theory. Furthermore, we explicitly compute the commutative Frobenius algebras that classify the restrictions of the extended theories to circles and bordisms between them.
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