Unitary Categorical Symmetries

Thomas Bartsch

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arXiv · 2502.04440

Unitary Categorical Symmetries

Thomas Bartsch

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Abstract

Global invertible symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to non-invertible symmetries by considering unitary actions of higher fusion category symmetries $\mathcal{C}$ on twisted sector local operators. We propose that the latter transform in $\ast$-representations of the tube algebra associated to $\mathcal{C}$, which we introduce and classify using the notion of higher $S$-matrices of higher braided fusion categories.

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Thomas Bartsch. 2025-02-06. Unitary Categorical Symmetries. https://arxiv.org/abs/2502.04440

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