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arXiv 2007.04969hep-th
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整体双场论之谜：开放问题和更高卡鲁扎-克莱因观点的情况

The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective

Luigi Alfonsi

备注：
62 pages, 1 figure, 2 tables; improved review of doubled-yet-gauged space, added references
发表信息：
Fortschr. Phys. 2021, 2000102
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摘要：

双场论几何的历史就是弦理论家努力驯服更高几何结构的历史。在这种精神下，本文的第一部分将简要概述DFT几何的文献，重点放在一个全球性的描述的尝试。在arXiv：1912.07089 [hep-th]中，我们提出了整体二重空间不是流形，而是丛gerbe的全空间。这意味着DFT是一个关于丛格的场论，类似于普通的卡鲁扎-克莱因理论是一个关于主丛的场论。在本文中，我们使arXiv：1912.07089 [hep-th]的原始构造更加直接。这是通过引入一个地图集的束gerbe。这个地图集自然配备了$2d$维局部图，其中$d$是物理时空的维度。我们认为，该地图集的本地图表应确定与通常的坐标描述DFT。在最后一部分，我们将讨论张量层次的整体几何方面在这个束gerbe图片。这允许识别它们的全局非几何性质，并解释非阿贝尔弦丛的图像是如何出现的。我们解释的阿贝尔T-折叠和Poisson-Lie的T-折叠作为整体张量族。

英文摘要：

The history of the geometry of Double Field Theory is the history of string theorists' effort to tame higher geometric structures. In this spirit, the first part of this paper will contain a brief overview on the literature of geometry of DFT, focusing on the attempts of a global description. In arXiv:1912.07089 [hep-th] we proposed that the global doubled space is not a manifold, but the total space of a bundle gerbe. This would mean that DFT is a field theory on a bundle gerbe, in analogy with ordinary Kaluza-Klein Theory being a field theory on a principal bundle. In this paper we make the original construction by arXiv:1912.07089 [hep-th] significantly more immediate. This is achieved by introducing an atlas for the bundle gerbe. This atlas is naturally equipped with $2d$-dimensional local charts, where $d$ is the dimension of physical spacetime. We argue that the local charts of this atlas should be identified with the usual coordinate description of DFT. In the last part we will discuss aspects of the global geometry of tensor hierarchies in this bundle gerbe picture. This allows to identify their global non-geometric properties and explain how the picture of non-abelian String-bundles emerges. We interpret the abelian T-fold and the Poisson-Lie T-fold as global tensor hierarchies.

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