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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2019-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.1.033054 |
| _version_ | 1797211687621754880 |
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| author | Wenjie Ji Xiao-Gang Wen |
| author_facet | Wenjie Ji Xiao-Gang Wen |
| author_sort | Wenjie Ji |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:30:27Z |
| format | Article |
| id | doaj.art-9dd685c714ca46fb8f315f944833fe72 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:30:27Z |
| publishDate | 2019-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-9dd685c714ca46fb8f315f944833fe722024-04-12T16:46:27ZengAmerican Physical SocietyPhysical Review Research2643-15642019-10-011303305410.1103/PhysRevResearch.1.033054Noninvertible anomalies and mapping-class-group transformation of anomalous partition functionsWenjie JiXiao-Gang WenRecently, 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.http://doi.org/10.1103/PhysRevResearch.1.033054 |
| spellingShingle | Wenjie Ji Xiao-Gang Wen Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions Physical Review Research |
| title | Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions |
| title_full | Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions |
| title_fullStr | Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions |
| title_full_unstemmed | Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions |
| title_short | Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions |
| title_sort | noninvertible anomalies and mapping class group transformation of anomalous partition functions |
| url | http://doi.org/10.1103/PhysRevResearch.1.033054 |
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