Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916018533695488 |
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| author | Haake, Benjamin |
| author_facet | Haake, Benjamin |
| contents | We study the gauging of invertible symmetries, particularly in 3 dimensions, using equivariantisation, $G$-crossed braided zesting, and the generalised orbifold construction. We discuss how these methods are related and illustrate them in various examples. We cover all $\mathbb{Z}_2$-symmetries in Dijkgraaf--Witten $\mathbb{Z}_2$-gauge theory $\mathcal{D}(\mathbb{Z}_2)$, the $\mathbb{Z}_2$-symmetries described by Tambara--Yamagami categories, and obstructions to gauging the central symmetry in Chern--Simons $\mathrm{SU}(2)_k$-gauge theory. We introduce zested orbifold data for symmetries related by zesting and show that the two associated orbifold data are Morita-equivalent, i.e.\ they have the same underlying surface defect. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation Haake, Benjamin High Energy Physics - Theory Mathematical Physics Quantum Algebra We study the gauging of invertible symmetries, particularly in 3 dimensions, using equivariantisation, $G$-crossed braided zesting, and the generalised orbifold construction. We discuss how these methods are related and illustrate them in various examples. We cover all $\mathbb{Z}_2$-symmetries in Dijkgraaf--Witten $\mathbb{Z}_2$-gauge theory $\mathcal{D}(\mathbb{Z}_2)$, the $\mathbb{Z}_2$-symmetries described by Tambara--Yamagami categories, and obstructions to gauging the central symmetry in Chern--Simons $\mathrm{SU}(2)_k$-gauge theory. We introduce zested orbifold data for symmetries related by zesting and show that the two associated orbifold data are Morita-equivalent, i.e.\ they have the same underlying surface defect. |
| title | Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2605.16942 |