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Braidings on topological operators, anomaly of higher-form symmetries and the SymTFT (2503.13633v1)

Published 17 Mar 2025 in hep-th, cond-mat.str-el, math-ph, math.MP, and math.QA

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.

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