Topological defect lines in two dimensional fermionic CFTs
We consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.5.216 |
| _version_ | 1797448393067331584 |
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| author | Chi-Ming Chang, Jin Chen, Fengjun Xu |
| author_facet | Chi-Ming Chang, Jin Chen, Fengjun Xu |
| author_sort | Chi-Ming Chang, Jin Chen, Fengjun Xu |
| collection | DOAJ |
| description | We consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of TDLs, called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing feature is an extra one-dimensional Majorana fermion living on the worldline of the TDLs. The properties of TDLs in fermionic CFTs are captured in the mathematical language of the super fusion category. We propose a classification of the rank-2 super fusion categories generalizing the $\mathbb{Z}_8$ classification for the anomalies of $\mathbb{Z}_2$ symmetries. We explicitly solve the F-moves for all the nontrivial categories, and derive the corresponding spin selection rules that constrain the spectrum of the defect operators. We find the full set of TDLs in the standard fermionic minimal models and a partial set of TDLs in the two exceptional models, which give CFT realizations to the rank-2 super fusion categories. Finally, we discuss a constraint on the renormalization group flow that preserves a q-type TDL. |
| first_indexed | 2024-03-09T14:09:41Z |
| format | Article |
| id | doaj.art-4c75fdd8b997401491c3f5de8edc9f0b |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-09T14:09:41Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-4c75fdd8b997401491c3f5de8edc9f0b2023-11-29T12:33:50ZengSciPostSciPost Physics2542-46532023-11-0115521610.21468/SciPostPhys.15.5.216Topological defect lines in two dimensional fermionic CFTsChi-Ming Chang, Jin Chen, Fengjun XuWe consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of TDLs, called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing feature is an extra one-dimensional Majorana fermion living on the worldline of the TDLs. The properties of TDLs in fermionic CFTs are captured in the mathematical language of the super fusion category. We propose a classification of the rank-2 super fusion categories generalizing the $\mathbb{Z}_8$ classification for the anomalies of $\mathbb{Z}_2$ symmetries. We explicitly solve the F-moves for all the nontrivial categories, and derive the corresponding spin selection rules that constrain the spectrum of the defect operators. We find the full set of TDLs in the standard fermionic minimal models and a partial set of TDLs in the two exceptional models, which give CFT realizations to the rank-2 super fusion categories. Finally, we discuss a constraint on the renormalization group flow that preserves a q-type TDL.https://scipost.org/SciPostPhys.15.5.216 |
| spellingShingle | Chi-Ming Chang, Jin Chen, Fengjun Xu Topological defect lines in two dimensional fermionic CFTs SciPost Physics |
| title | Topological defect lines in two dimensional fermionic CFTs |
| title_full | Topological defect lines in two dimensional fermionic CFTs |
| title_fullStr | Topological defect lines in two dimensional fermionic CFTs |
| title_full_unstemmed | Topological defect lines in two dimensional fermionic CFTs |
| title_short | Topological defect lines in two dimensional fermionic CFTs |
| title_sort | topological defect lines in two dimensional fermionic cfts |
| url | https://scipost.org/SciPostPhys.15.5.216 |
| work_keys_str_mv | AT chimingchangjinchenfengjunxu topologicaldefectlinesintwodimensionalfermioniccfts |