Non-invertible symmetry enriched string net topological orders
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918528155648000 |
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| author | Eck, Luisa Huston, Peter Kawagoe, Kyle Penneys, David |
| author_facet | Eck, Luisa Huston, Peter Kawagoe, Kyle Penneys, David |
| contents | We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as anyon condensation. In both cases, the NI-SETO is a relative center of UFCs. All NI-SETOs can be realized in either model, where we can use enriched UFCs to get chiral examples on the boundary of a 3D Walker-Wang model representing the anomaly. We describe several examples of NI-SETOs and compute the qualitative symmetry action on anyons and symmetry defects using tube algebra techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-invertible symmetry enriched string net topological orders Eck, Luisa Huston, Peter Kawagoe, Kyle Penneys, David Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra Quantum Physics We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as anyon condensation. In both cases, the NI-SETO is a relative center of UFCs. All NI-SETOs can be realized in either model, where we can use enriched UFCs to get chiral examples on the boundary of a 3D Walker-Wang model representing the anomaly. We describe several examples of NI-SETOs and compute the qualitative symmetry action on anyons and symmetry defects using tube algebra techniques. |
| title | Non-invertible symmetry enriched string net topological orders |
| topic | Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra Quantum Physics |
| url | https://arxiv.org/abs/2605.28794 |