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arXiv 1908.08086hep-thmath-phmath.MP
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关于M5-Brane模型II:度量弦结构

Towards an M5-Brane Model II: Metric String Structures

Christian Saemann, Lennart Schmidt

摘要:

在本文中,我们发展了度量弦结构的数学公式。这些在某些六维超共形场论的表述中起着至关重要的作用,我们相信它们也是(2,0)-理论未来潜在表述的基础。我们发现,通常在文献中介绍的非阿贝尔gerbes的连接是有问题的,因为它们是局部规范等价的阿贝尔gerbes的连接。字符串结构上的连接形成一个例外,我们介绍了一个调整后的Weil代数的一般概念,导致潜在的相互作用的连接更高的主束。考虑一种特殊情况,我们给出了弦结构的度量扩张和相应的调整Weil代数。后者导致以前在测量超重力的背景下手工构建的连接。我们还解释了如何在规范超引力嵌入张量诱导莱布尼茨代数适合我们的图片。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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