In this paper, we develop the mathematical formulation of metric string structures. These play a crucial role in the formulation of certain six‐dimensional superconformal field theories and we believe that they also underlie potential future formulations of the (2,0)‐theory. We show that the connections on non‐abelian gerbes usually introduced in the literature are problematic in that they are locally gauge equivalent to connections on abelian gerbes. Connections on string structures form an exception and we introduce the general concept of an adjusted Weil algebra leading to potentially interacting connections on higher principal bundles. Considering a special case, we derive the metric extension of string structures and the corresponding adjusted Weil algebra. The latter lead to connections that were previously constructed by hand in the context of gauged supergravities. We also explain how the Leibniz algebras induced by an embedding tensor in gauged supergravities fit into our picture.

中文翻译：

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迈向M5-Brane模型II：公制琴弦结构

在本文中，我们开发了度量字符串结构的数学公式。这些在某些六维超保形场论的制定中起着至关重要的作用，我们相信它们也构成了（2,0）理论未来潜在表述的基础。我们表明，文献中通常介绍的非阿贝拉格布人的联系存在问题，因为它们在局部尺度上等同于阿贝拉格布人的联系。字符串结构上的连接构成一个例外，我们介绍了调整后的Weil代数的一般概念，从而导致了较高主体束上潜在的相互作用。考虑到特殊情况，我们导出了字符串结构的度量扩展以及相应的调整后的Weil代数。后者导致以前在手工测量的超重力环境中构建的连接。我们还解释了在测量的超重力中嵌入张量引起的莱布尼兹代数如何适合我们的图片。