论文标题
建模Landau-Ginzburg模型之间的接口因素作为模块函子
Modelling interface factorizations between Landau-Ginzburg models as module functors
论文作者
论文摘要
我们研究n =（2,2）超对称兰道吉堡模型之间的B型接口的融合。这些接口可以通过矩阵因子差的矩阵因素化来描述，它们的融合是通过因子化的张量产物来建模的。融合固定界面的效果会引起函数对矩阵因数化类别的效果。对于至少一些接口，可以将其提升为多项式环上模块类别的函子。这些融合函数提供了一种替代方法，可以在Landau-Ginzburg模型之间建模界面，该模型以其融合性能来表征接口。界面场对应于可以通过Hochschild型的同胞来定义的融合函子之间的形态。这导致了融合函子的严格单体超类别，其中水平组成是通过函子组成给出的。 Fusion函子的类别可以与映射Fusion Foundor映射到相应界面分解的函数的矩阵因法化类别有关。它不是忠实的，但是我们证明了一个变量中的多项式环已经满了。在融合函数方面对接口的描述具有一个优势，即接口的融合变得简单。它提供了一种计算工具来评估矩阵因子化的张量产品，例如在Kazama-Suzuki模型中应用，以分析合理缺陷的融合类别，或在Khovanov-Rozansky Link同源性的背景下。
We study the fusion of B-type interfaces between N=(2,2) supersymmetric Landau-Ginzburg models. Such interfaces can be described by matrix factorizations of the difference of the superpotentials, and their fusion is modelled by the tensor product of the factorizations. The effect of fusing a fixed interface gives rise to a functor on the category of matrix factorizations. For at least some interfaces, this can be lifted to a functor on the category of modules over polynomial rings. These fusion functors provide an alternative way of modelling interfaces between Landau-Ginzburg models that characterizes interfaces by their fusion properties. Interface fields correspond to morphisms between fusion functors that can be defined via a Hochschild-type cohomology. This leads to a strict monoidal supercategory of fusion functors, where horizontal composition is given by composition of functors. The category of fusion functors can be related to the category of matrix factorizations by a functor that maps a fusion functor to the corresponding interface factorization. It is not faithful, but we prove that it is full for polynomial rings in one variable. The description of interfaces in terms of fusion functors has the advantage that fusion of interfaces becomes simple. It provides a computational tool to evaluate tensor products of matrix factorizations, and could be applied for example in Kazama-Suzuki models to analyse fusion categories of rational defects, or in the context of Khovanov-Rozansky link homology.
