Soft symmetries of topological orders

• URL: http://arxiv.org/abs/2501.03314v2
• Date: Wed, 22 Jan 2025 02:27:14 GMT
• Title: Soft symmetries of topological orders
• Authors: Ryohei Kobayashi, Maissam Barkeshli,
• Abstract summary: (2+1)D topological orders possess emergent symmetries given by a group $textAut(mathcalC)$. In this paper we discuss cases where $textAut(mathcalC)$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial.
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• Abstract: (2+1)D topological orders possess emergent symmetries given by a group $\text{Aut}(\mathcal{C})$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we discuss cases where $\text{Aut}(\mathcal{C})$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged SPT states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, non-invertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. We also demonstrate analogous phenomena in higher dimensions, such as (3+1)D gauge theory with gauge group given by the quaternion group $Q_8$.

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