标题： 广义双重结构在规范双重场理论中的应用 显示英文标题

标题： Extended Doubled Structures of Algebroids for Gauged Double Field Theory

摘要： 我们研究了与规范双场理论（DFT）相关的代数结构的德林费尔德双的类似物，该理论涉及$O(D,D+n)$。 我们表明，在规范DFT中由扭曲的C括号定义的代数结构是由三个（扭曲）李代数结构的直和构成的。 它们表现出一种“三重”，我们称之为扩展双，而不是在（未规范）DFT中出现的“双重”结构。 我们发现扩展双结构的相容性不仅导致强约束，还导致规范DFT中的额外条件。 我们在一个$(2D+n)$维乘积流形中建立了这些结构的几何实现，并检查了它们与杂化弦理论的广义几何以及DFT中非阿贝尔规范对称性的关系。 显示英文摘要

摘要： We study an analogue of the Drinfel'd double for algebroids associated with the $O(D,D+n)$ gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three (twisted) Lie algebroids. They exhibit a "tripled", which we call the extended double, rather than the "doubled" structure appeared in (ungauged) DFT. We find that the compatibilities of the extended doubled structure result not only in the strong constraint but also the additional condition in the gauged DFT. We establish a geometrical implementation of these structures in a $(2D+n)$-dimensional product manifold and examine the relations to the generalized geometry for heterotic string theories and non-Abelian gauge symmetries in DFT.