论文标题
平滑的2组扩展和捆扎胶的对称性
Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
论文作者
论文摘要
我们研究了捆绑的gerbes，上面是$ m $，该$ m $带有连接的谎言组$ g $的动作。我们表明，这些数据产生了平滑的2组$ g $的2组扩展，这是$ m $的光滑的2组Hermitean Line捆绑包。这种2组扩展对束gerbe上的模棱两可的结构进行了分类，其非平凡性构成了对均衡结构的存在的阻碍。我们提出了一种新的全球方法，用于与连接的捆绑包Gerbe并行运输，并使用它的替代性结构，以相关捆绑构造的同拷贝 - 辅助版本为单位。我们将结果应用于量子力学中的非缔合磁翻译和Faddeev-Mickelsson-Shatashvili异常的新描述。我们还建议在几何框架内的平滑字符串2组模型的定义。从一个紧凑的简单连接的Lie Group $ G $开始，我们证明，由我们的构造产生的平滑2组扩展名为$ G $的字符串组提供了新的型号。
We study bundle gerbes on manifolds $M$ that carry an action of a connected Lie group $G$. We show that these data give rise to a smooth 2-group extension of $G$ by the smooth 2-group of hermitean line bundles on $M$. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev-Mickelsson-Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-group models within our geometric framework. Starting from a basic gerbe on a compact simply-connected Lie group $G$, we prove that the smooth 2-group extensions of $G$ arising from our construction provide new models for the string group of $G$.
