论文标题
截短的仿射Rozansky- witten模型作为扩展的TQFTS
Truncated affine Rozansky--Witten models as extended TQFTs
论文作者
论文摘要
我们构建了与Rozansky关联的扩展TQFTS-具有目标歧管的WITTEN模型$ T^*\ MATHBB {C}^n $。构造的起点是其对象是如此的Rozansky的三类模型，其形态是所有复合的缺陷。通过截断，我们获得了散装理论，表面缺陷和线缺陷类别类别的（非偏simimple）2类别$ \ MATHCAL {C} $。通过系统的系统应用，我们构建了一个唯一的二维扩展二维tqft，该TQFT在$ \ Mathcal {c} $中构建了每个Aggine Rozansky-Witten模型。通过在封闭表面上评估此TQFT，我们获得了最初的3维理论的无限维状态空间（按风味和R-Charge分级）。此外，我们明确地计算了交换性的Frobenius代数，该代数将扩展理论的限制分类为它们之间的圆圈和界异教。
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.
