Algebroid structures on para-Hermitian manifolds
Algebroid structures on para-Hermitian manifolds
复制标题
拟厄米流形上的代数体结构
DOI：
10.1063/1.5040263
复制
发表时间：
2018
影响因子：
1.3
通讯作者：
D. Svoboda
中科院分区：
文献类型：
--
作者：
D. Svoboda
我们提出了双场论 (DFT) 物理文献中出现的所谓 D 括号的全局构造，并表明如果满足某些可积性标准，它可以被视为两个库朗代数体括号的和。特别是，我们证明了 DFT 中使用的扩展时空的局部图像自然地适合准厄米流形的几何框架，并且（几乎）准厄米流形的数据足以构造 D 括号。此外，DFT 中出现的括号的扭曲可以在该框架中从几何角度解释为底层准厄米结构的某些变形的结果。
We present a global construction of a so-called D-bracket appearing in the physics literature of Double Field Theory (DFT) and show that if certain integrability criteria are satisfied, it can be seen as a sum of two Courant algebroid brackets. In particular, we show that the local picture of the extended space-time used in DFT fits naturally in the geometrical framework of para-Hermitian manifolds and that the data of an (almost) para-Hermitian manifold is sufficient to construct the D-bracket. Moreover, the twists of the bracket appearing in DFT can be interpreted in this framework geometrically as a consequence of certain deformations of the underlying para-Hermitian structure.