Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions
Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions
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DOI：
10.1103/physrevresearch.1.033054
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发表时间：
2019-05
影响因子：
4.2
通讯作者：
Wenjie Ji;X. Wen
中科院分区：
文献类型：
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作者：
Wenjie Ji;X. Wen
最近，人们认识到反常现象可以完全按一维的拓扑序、对称保护拓扑(SPT)序和对称丰富的拓扑序来分类。人们过去研究的反常现象是对应于一维可逆拓扑序和/或对称保护拓扑序的可逆反常。本文引入了不可逆反常的概念，刻画了一般拓扑序的边界。不可逆异常的一个关键特征是它具有多个配分函数。在时空的映射类群变换下，这些配分函数以其对应的高维拓扑阶数据为特征进行一定的变换。实际上，反常配分函数的变换方式与高维对应的拓扑序的简并基态相同。这种不可逆异常的一般理论可能会有广泛的应用。作为例子，我们证明了2+1D双半离子(DS)拓扑序的不可约无间隙边界必有中心电荷$c=\bar c\geq\frac{25}{28}$.
Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to study are invertible anomalies that correspond to invertible topological orders and/or symmetry protected topological orders in one higher dimension. In this paper, we introduce a notion of non-invertible anomaly, which describes the boundary of generic topological order. A key feature of non-invertible anomaly is that it has several partition functions. Under the mapping class group transformation of space-time, those partition functions transform in a certain way characterized by the data of the corresponding topological order in one higher dimension. In fact, the anomalous partition functions transform in the same way as the degenerate ground states of the corresponding topological order in one higher dimension. This general theory of non-invertible anomaly may have wide applications. As an example, we show that the irreducible gapless boundary of 2+1D double-semion (DS) topological order must have central charge $c=\bar c \geq \frac{25}{28}$.