D-膜上的拓扑绝缘体和超导体
Topological Insulators and Superconductors from D-branes
摘要：
提出了用弦论中的D-膜来实现拓扑绝缘体和超导体，如量子自旋霍尔效应和Z_2拓扑绝缘体。我们建立了TI/TSC的K理论分类和D膜电荷之间的一一对应关系。TI和TSC的弦论实现自然地伴随着规范相互作用，而D膜的Wess-Zumino项产生了拓扑性质的规范场。这揭示了非相互作用系统之外的TI和TSC，以及其基础拓扑场论描述。特别是，我们的弦论实现包括两个空间维度的蜂窝格子Kitaev模型，以及它的高维扩展。
英文摘要：
Realization of topological insulators (TIs) and superconductors (TSCs), such as the quantum spin Hall effect and the Z_2 topological insulator, in terms of D-branes in string theory is proposed. We establish a one-to-one correspondence between the K-theory classification of TIs/TSCs and D-brane charges. The string theory realization of TIs and TSCs comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature. This sheds light on TIs and TSCs beyond non-interacting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions.
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