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.

我们研究了歧管M上的束gerbes，这些歧管承载着一个相连的李群G的作用。我们显示这些数据通过M上的Hermitean线束的光滑2群引起G的光滑2群扩展。该2组扩展对捆gerbe上的等变结构进行分类，其非平凡性阻碍了等变结构的存在。我们提出了一种新的全局方法，用于并行连接带连接的捆gerbe，并根据相关捆结构的同伦相干版本，使用它提供了这种平滑的2-group扩展的替代结构。我们应用我们的结果对量子力学中的非缔合磁性平移以及量子场论中的Faddeev-Mickelsson-Shatashvili异常进行了新的描述。我们还提出了在几何框架内定义平滑字符串2组模型的定义。从紧紧连接的李群G上的基本gerbe开始，我们证明了的光滑2群扩展摹从我们的建设产生提供了弦乐群的新车型摹。