Aybike Çatal-Özer, Keremcan Doğan, Cem Yetişmişoğlu
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引用次数: 0
摘要
我们为弦理论和 M 理论中使用的更一般的括号结构扩展了列双曲面的概念。我们正式提出了关于弧基的微积分和对偶计算的概念。为此,我们重新解释了莱布尼兹网格匹配对的主要结果。通过研究一组相当普遍的基本阿格布洛公理,我们提出了向量束上两个不具有通常意义上的对偶性的微积分之间的相容条件。给定两个配备了满足相容条件的计算器的实体,我们在它们的直接和上构造其双。这概括了李双桥的德林费尔德双桥。我们讨论了文献中的几个例子,包括例外库朗括号。利用南布-泊松结构,我们构建了一个从物理和数学角度来看都很重要的明确例子。这个例子可以看作是三角烈列双曲面在高库仑括号领域的扩展,它自动满足相容条件。我们通过定义南布-泊松例外广义几何来扩展泊松广义几何,并在此框架内证明了一些初步结果。我们还对形式rackoids 框架中的全局图进行了评论,并对向量束值度量的概念稍作扩展。
Drinfel’d double of bialgebroids for string and M theories: dual calculus framework
We extend the notion of Lie bialgebroids for more general bracket structures used in string and M theories. We formalize the notions of calculus and dual calculi on algebroids. We achieve this by reinterpreting the main results of the matched pairs of Leibniz algebroids. By examining a rather general set of fundamental algebroid axioms, we present the compatibility conditions between two calculi on vector bundles which are not dual in the usual sense. Given two algebroids equipped with calculi satisfying the compatibility conditions, we construct its double on their direct sum. This generalizes the Drinfel’d double of Lie bialgebroids. We discuss several examples from the literature including exceptional Courant brackets. Using Nambu-Poisson structures, we construct an explicit example, which is important both from physical and mathematical point of views. This example can be considered as the extension of triangular Lie bialgebroids in the realm of higher Courant algebroids, that automatically satisfy the compatibility conditions. We extend the Poisson generalized geometry by defining Nambu-Poisson exceptional generalized geometry and prove some preliminary results in this framework. We also comment on the global picture in the framework of formal rackoids and we slightly extend the notion for vector bundle valued metrics.
期刊介绍:
The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal.
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