拓扑相的M-理论成因
M-theoretic Genesis of Topological Phases
摘要：
通过建立（2+1）维拓扑场论与非双曲三维流形之间的对应关系，提出了一种新的构造和分类物质任意子拓扑相的M-理论方法.在这个构造中，拓扑相出现为包裹在某些类型的非双曲3-流形周围的M5-膜的宏观世界体积理论。我们设计了一个系统的算法，用于从内部包裹三维流形的拓扑数据中识别出涌现拓扑相。作为我们的方法的基准，我们再现所有已知的酉玻色子拓扑秩序的秩4。值得注意的是，我们的建设并不限于一个单一的玻色子理论，但它也可以产生费米和/或非酉拓扑相位在一个等效的方式。从而为物质拓扑相的分类开辟了一条新的途径。
英文摘要：
We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction, the topological phases emerge as macroscopic world-volume theories of M5-branes wrapped around certain types of non-hyperbolic 3-manifolds. We devise a systematic algorithm for identifying the emergent topological phases from topological data of the internal wrapped 3-manifolds. As a benchmark of our approach, we reproduce all the known unitary bosonic topological orders up to rank 4. Remarkably, our construction is not restricted to an unitary bosonic theory but it can also generate fermionic and/or non-unitary topological phases in an equivalent fashion. Hence, we pave a new route toward the classification of topological phases of matter.
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