2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914579713359872 |
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| author | Carqueville, Nils Haake, Benjamin |
| author_facet | Carqueville, Nils Haake, Benjamin |
| contents | A large class of symmetries of topological quantum field theories is naturally described by functors into higher categories of topological defects. Here we study 2-group symmetries of 3-dimensional TQFTs. We explain that these symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data. In the special case of Reshetikhin-Turaev theories coming from $G$-crossed braided fusion categories $\mathcal C^\times_G$, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form $G$-symmetry on the neutral component $\mathcal C_e$ of $\mathcal C^\times_G$ produces its equivariantisation $(\mathcal C^\times_G)^G$, which in turn features a generalised symmetry whose gauging recovers $\mathcal C_e$. If $G$ is commutative, the latter symmetry reduces to a 1-form symmetry involving the Pontryagin dual group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08178 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging Carqueville, Nils Haake, Benjamin Quantum Algebra High Energy Physics - Theory Mathematical Physics A large class of symmetries of topological quantum field theories is naturally described by functors into higher categories of topological defects. Here we study 2-group symmetries of 3-dimensional TQFTs. We explain that these symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data. In the special case of Reshetikhin-Turaev theories coming from $G$-crossed braided fusion categories $\mathcal C^\times_G$, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form $G$-symmetry on the neutral component $\mathcal C_e$ of $\mathcal C^\times_G$ produces its equivariantisation $(\mathcal C^\times_G)^G$, which in turn features a generalised symmetry whose gauging recovers $\mathcal C_e$. If $G$ is commutative, the latter symmetry reduces to a 1-form symmetry involving the Pontryagin dual group. |
| title | 2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.08178 |