Fusion category symmetries in 1+1D QFTs are used to describe anomalies and classify gapped phases via boundary conditions of 2+1D models and gauge-theoretic techniques for self-dual cases.
Verlinde, and Herman L
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Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
Fusion category symmetries in 1+1D QFTs are used to describe anomalies and classify gapped phases via boundary conditions of 2+1D models and gauge-theoretic techniques for self-dual cases.