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arXiv · 2605.16942

Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation

Benjamin Haake
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Abstract

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.

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Benjamin Haake. 2026-05-16. Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation. https://arxiv.org/abs/2605.16942

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