关于T-对偶的拓扑
On the topology of T-duality
摘要：
在弦理论中，引入了同一底空间B上两个主U（1）-丛E_1和E_2之间的T-对偶概念，以及上同调类$h_1\in H^3(E_1)$和$h_2\in H^3(E_2)$。T-对偶的主要优点之一是$E_1$的$h_1$ -扭曲K-理论与$E_2$的$h_2$ -扭曲K-理论同构。本文引入了一个新的非常拓扑的T-对偶概念。本文从拓扑学的角度对（E，h）进行了研究，并构造了一个分类空间。利用这一点，我们构造了一个通用的对偶对一个给定的对。我们的构造立即给出了对偶的一些已知和新的性质。特别是它意味着存在一个对偶的任何对（E，h），它还描述了模糊性，直到对偶是明确的。为了处理扭曲的K-理论，需要一些照顾，特别是在处理自然性问题时，因为扭曲的K-理论依赖于扭曲和扭曲理论的显式模型-照顾在一些现有的文献中缺失。我们说明了使用的T-对偶的扭曲K-群的一些明确的计算。
英文摘要：
In string theory, the concept of T-duality between two principal U(1)-bundles E_1 and E_2 over the same base space B, together with cohomology classes $h_1\in H^3(E_1)$ and $h_2\in H^3(E_2)$, has been introduced. One of the main virtues of T-duality is that $h_1$-twisted K-theory of $E_1$ is isomorphic to $h_2$-twisted K-theory of $E_2$. In this paper, a new, very topological concept of T-duality is introduced. The study pairs (E,h) as above from a topological point of view and construct a classifying space of such pairs. Using this, we construct a universal dual pair to a given pair. Our construction immediately gives a number of known and new properties of the dual. In particular it implies existence of a dual of any pair (E,h), and it also describes the ambiguity upto which the dual is well defined. In order to deal with twisted K-theory, some care is needed, in particular when dealing with naturality questions, because the twisted K-theory depends on the explicit model for the twists and the twisted theory --care which is missing in some of the existing literature. We illustrate the use of T-duality by some explicit calculations of twisted K-groups.
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