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Braidings on topological operators, anomaly of higher-form symmetries and the SymTFT
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abstract
The anomaly of non-invertible higher-form symmetries is determined by the braiding of topological operators implementing them. In this paper, we study a method to classify braidings on topological line and surface operators by leveraging the fact that topological operators which admit a braiding are symmetries of their associated SymTFT. This perspective allows us to formulate an algorithm to explicitly compute all possible braidings on a given fusion category, bypassing the need to solve the hexagon equations. Additionally, using 3+1d SymTFTs, we determine braidings on various fusion 2-categories. We prove a necessary and sufficient condition for the fusion 2-categories $\Sigma \mathcal{C}$, 2Vec$_G^{\pi}$ and Tambara-Yamagami (TY) 2-categories TY$(A,\pi)$ to admit a braiding.
Forward citations
Cited by 2 Pith papers
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Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism
For G=(Z2,Z2,triv,1), the authors classify anomalies via oriented and spin bordism in spacetime dimensions d<=5 and derive the (3+1)D SymTFT boundary conditions, including the equivalence of the anomalous symmetry cat...
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Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.
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