Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions
Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to study are invertible anomalies that correspond to invertible topolog...
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Veröffentlicht in: | Physical review research 2019-10, Vol.1 (3), p.033054, Article 033054 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological 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 noninvertible anomaly, which describes the boundary of generic topological order. It is characterized by two features. First, a theory with noninvertible anomaly has a multicomponent partition function. Second, under the mapping class group transformation of space-time, the vector of partition functions transform covariantly. 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 noninvertible anomaly may have wide applications. As an example, we show that the irreducible gapless boundary of 2+1D double-semion topological order must have central charge c=c[over ¯]>25/28. |
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ISSN: | 2643-1564 2643-1564 |
DOI: | 10.1103/PhysRevResearch.1.033054 |