论文标题
全球双场理论的难题：开放问题和更高的Kaluza-Klein观点的案例
The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective
论文作者
论文摘要
双场理论的几何形状的历史是弦理论家驯服更高几何结构的努力的历史。本着这种精神，本文的第一部分将包含有关DFT几何文献的简要概述，重点是全球描述的尝试。在Arxiv：1912.07089 [Hepth]我们提出，全球双倍的空间不是多种多样，而是束Gerbe的总空间。这意味着DFT是捆绑捆绑的现场理论，与普通的Kaluza-Klein理论类似，是主要捆绑包的现场理论。在本文中，我们制作了Arxiv的原始结构：1912.07089 [HEP-TH]明显更直接。这是通过引入捆绑包Gerbe的地图集来实现的。该地图集自然配备了$ 2D $维的本地图表，其中$ d $是物理时空的尺寸。我们认为，该地图集的本地图表应与DFT的通常坐标描述一起识别。在最后一部分中，我们将讨论此捆绑图片中张量层次结构的全局几何形状的各个方面。这允许识别其全局非几何属性，并解释非亚伯弦捆绑的图片如何出现。我们将Abelian T折和泊松lie T折解释为全球张量层次结构。
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.
