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arXiv · 2503.13633

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

Pavel Putrov·Rajath Radhakrishnan
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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.

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Pavel Putrov, Rajath Radhakrishnan. 2025-03-17. Braidings on topological operators, anomaly of higher-form symmetries and the SymTFT. https://arxiv.org/abs/2503.13633

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