Non-invertible symmetry webs
Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with $\mathcal{G...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
SciPost
2023
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| _version_ | 1826312743992426496 |
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| author | Bhardwaj, L Bottini, LE Schäfer-Nameki, S Tiwari, A |
| author_facet | Bhardwaj, L Bottini, LE Schäfer-Nameki, S Tiwari, A |
| author_sort | Bhardwaj, L |
| collection | OXFORD |
| description | Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with
$\mathcal{G}$
0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [SciPost Phys. 15, 122 (2023)]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups
$\mathcal{G}$, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions. |
| first_indexed | 2024-04-23T08:25:07Z |
| format | Journal article |
| id | oxford-uuid:1dca0b6f-c96b-458f-83c4-9c8bcbd4e6e3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-04-23T08:25:07Z |
| publishDate | 2023 |
| publisher | SciPost |
| record_format | dspace |
| spelling | oxford-uuid:1dca0b6f-c96b-458f-83c4-9c8bcbd4e6e32024-04-16T09:09:27ZNon-invertible symmetry websJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1dca0b6f-c96b-458f-83c4-9c8bcbd4e6e3EnglishSymplectic ElementsSciPost2023Bhardwaj, LBottini, LESchäfer-Nameki, STiwari, ANon-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with $\mathcal{G}$ 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [SciPost Phys. 15, 122 (2023)]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups $\mathcal{G}$, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions. |
| spellingShingle | Bhardwaj, L Bottini, LE Schäfer-Nameki, S Tiwari, A Non-invertible symmetry webs |
| title | Non-invertible symmetry webs |
| title_full | Non-invertible symmetry webs |
| title_fullStr | Non-invertible symmetry webs |
| title_full_unstemmed | Non-invertible symmetry webs |
| title_short | Non-invertible symmetry webs |
| title_sort | non invertible symmetry webs |
| work_keys_str_mv | AT bhardwajl noninvertiblesymmetrywebs AT bottinile noninvertiblesymmetrywebs AT schafernamekis noninvertiblesymmetrywebs AT tiwaria noninvertiblesymmetrywebs |