Braidings on topological operators, anomaly of higher-form symmetries and the SymTFT

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.

53 pages, 10 figures, 3 appendices

Cited by in corpus (1)

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