二重几何与预轨面的整体性质
Global Aspects of Doubled Geometry and Pre-rackoid
摘要：
分析了双场论（DFT）的几何结构C-括号和Vaisman（度量，预DFT）代数体的积分问题.我们引入了一个概念的前rackoid作为一个全球性的组一样的对象的无穷小代数体结构。我们提出了前齿条结构的几种实现。一种认识是，一个pre-rackoid的元素定义的余切路径沿双重叶理的仿厄米流形。另一种实现是DFT代数体的形式指数映射。我们表明，前齿条减少到一个齿条，这是积分的柯朗代数体时，施加DFT的强约束。最后，对于一个物理应用，我们展示了一个三维拓扑西格玛模型的（前）rackoid的实现。
英文摘要：
The integration problem of a C-bracket and a Vaisman (metric, pre-DFT) algebroid which are geometric structures of double field theory (DFT) is analyzed. We introduce a notion of a pre-rackoid as a global group-like object for an infinitesimal algebroid structure. We propose that several realizations of pre-rackoid structures. One realization is that elements of a pre-rackoid are defined by cotangent paths along doubled foliations in a para-Hermitian manifold. Another realization is proposed as a formal exponential map of the algebroid of DFT. We show that the pre-rackoid reduces to a rackoid that is the integration of the Courant algebroid when the strong constraint of DFT is imposed. Finally, for a physical application, we exhibit an implementation of the (pre-)rackoid in a three-dimensional topological sigma model.
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