Universal non-invertible symmetries
<p>It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a 1-category. We argue that for a <em>d&l...
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| Format: | Journal article |
| Language: | English |
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Wiley
2022
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| _version_ | 1826309164216877056 |
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| author | Bhardwaj, L Schäfer-Nameki, S Wu, J |
| author_facet | Bhardwaj, L Schäfer-Nameki, S Wu, J |
| author_sort | Bhardwaj, L |
| collection | OXFORD |
| description | <p>It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a 1-category. We argue that for a <em>d</em>-dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a $(d-1)$-category, which is formed out of lower-dimensional topological quantum field theories with the same 0-form symmetry. We study in detail a 2-categorical piece of this $(d-1)$-category described by 2d topological quantum field theories with 0-form symmetry. We further show that the objects of this 2-category are the recently discussed 2d condensation defects constructed from higher-gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher-form or higher-group symmetry also form a $(d-1)$-category formed out of lower-dimensional topological quantum field theories with that higher-form or higher-group symmetry. A particularly interesting case is that of the 2-category of dual symmetries associated to gauging of finite 2-group symmetries, as it describes non-invertible symmetries arising from gauging 0-form symmetries that act on $(d-3)$-form symmetries. Such non-invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non-invertible symmetries. We describe how our results can be applied to compute non-invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2-category formed by 2d condensation defects in any arbitrary quantum field theory.</p> |
| first_indexed | 2024-03-07T07:30:05Z |
| format | Journal article |
| id | oxford-uuid:3e95d649-ac60-4f33-a74e-0115862dfcdd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:30:05Z |
| publishDate | 2022 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:3e95d649-ac60-4f33-a74e-0115862dfcdd2023-01-11T09:54:06ZUniversal non-invertible symmetriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3e95d649-ac60-4f33-a74e-0115862dfcddEnglishSymplectic ElementsWiley2022Bhardwaj, LSchäfer-Nameki, SWu, J<p>It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a 1-category. We argue that for a <em>d</em>-dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a $(d-1)$-category, which is formed out of lower-dimensional topological quantum field theories with the same 0-form symmetry. We study in detail a 2-categorical piece of this $(d-1)$-category described by 2d topological quantum field theories with 0-form symmetry. We further show that the objects of this 2-category are the recently discussed 2d condensation defects constructed from higher-gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher-form or higher-group symmetry also form a $(d-1)$-category formed out of lower-dimensional topological quantum field theories with that higher-form or higher-group symmetry. A particularly interesting case is that of the 2-category of dual symmetries associated to gauging of finite 2-group symmetries, as it describes non-invertible symmetries arising from gauging 0-form symmetries that act on $(d-3)$-form symmetries. Such non-invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non-invertible symmetries. We describe how our results can be applied to compute non-invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2-category formed by 2d condensation defects in any arbitrary quantum field theory.</p> |
| spellingShingle | Bhardwaj, L Schäfer-Nameki, S Wu, J Universal non-invertible symmetries |
| title | Universal non-invertible symmetries |
| title_full | Universal non-invertible symmetries |
| title_fullStr | Universal non-invertible symmetries |
| title_full_unstemmed | Universal non-invertible symmetries |
| title_short | Universal non-invertible symmetries |
| title_sort | universal non invertible symmetries |
| work_keys_str_mv | AT bhardwajl universalnoninvertiblesymmetries AT schafernamekis universalnoninvertiblesymmetries AT wuj universalnoninvertiblesymmetries |