T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
复制标题
通过非交换拓扑实现具有 H 通量的环面丛的 T 对偶性，II：高维情况和 T 对偶群
DOI：
10.4310/atmp.1999.v3.n2.a5
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发表时间：
2022
影响因子：
1.5
通讯作者：
Jonathan Rosenberg
中科院分区：
文献类型：
--
作者：
V. Mathai;Jonathan Rosenberg
我们使用非交换拓扑来研究具有 H 通量的主环面丛的 T 对偶性。我们精确地描述何时存在“经典”T-对偶，即具有对偶 H 通量的对偶丛，以及何时 T-对偶必须是“非经典”，即非交换环面的连续场。这种对偶性伴随着扭曲 K 理论的同构，这是匹配 D 膜电荷所必需的，就像在经典情况下一样。在经典情况下得到的扭曲上同调同构在非经典情况下被扭曲循环同调同构所取代。论文的一个重要部分详细分析了拓扑T-对偶的分类空间，以及T-对偶群及其作用。 T-对偶可能的非唯一性问题可以通过 T-对偶群的作用来研究。
We use noncommutative topology to study T-duality for principal torus bundles with H-flux. We characterize precisely when there is a “classical” T-dual, i.e., a dual bundle with dual H-flux, and when the T-dual must be “non-classical,” that is, a continuous field of noncommutative tori. The duality comes with an isomorphism of twisted K -theories, re-quired for matching of D-brane charges, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced in the non-classical case by an isomorphism of twisted cyclic homology. An important part of the paper contains a detailed analysis of the classifying space for topological T-duality, as well as the T-duality group and its action. The issue of possible non-uniqueness of T-duals can be studied via the action of the T-duality group.