弦2-群的高次规范理论
Higher Gauge Theory with String 2-Groups
摘要：
以Schommer-Pries的弦2-群模型为结构2-群，给出了主2-丛上高次规范理论的运动学数据的完整而明确的描述.我们开始与李群胚，双丛和双丛态射的弱2-范畴Bibun自包含的审查。然后，我们构建范畴内部的Bibun，这使我们能够定义主2-束2-组内部的Bibun结构2-组。利用它们，我们对弦群的2-群模型进行了李微分，得到了著名的弦李2-代数。推广的微分过程中，我们发现Maurer-Cartan形式导致我们更高的非阿贝尔Deligne上同调，编码的运动学数据的高规范理论连同他们的（有限）规范对称性。最后，我们讨论一个非阿贝尔自对偶弦的例子。
英文摘要：
We give a complete and explicit description of the kinematical data of higher gauge theory on principal 2-bundles with the string 2-group model of Schommer-Pries as structure 2-group. We start with a self-contained review of the weak 2-category Bibun of Lie groupoids, bibundles and bibundle morphisms. We then construct categories internal to Bibun, which allow us to define principal 2-bundles with 2-groups internal to Bibun as structure 2-groups. Using these, we Lie-differentiate the 2-group model of the string group and we obtain the well-known string Lie 2-algebra. Generalizing the differentiation process, we find Maurer-Cartan forms leading us to higher non-abelian Deligne cohomology, encoding the kinematical data of higher gauge theory together with their (finite) gauge symmetries. We end by discussing an example of non-abelian self-dual strings in this setting.
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