An operator-algebraic framework proves that boundary conditions in (1+1)D gapped phases with categorical symmetry are classified by objects of the module category M_Q^op via an equivalence of categories, yielding a bulk-boundary correspondence as the enriched center.
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Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.
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Bulk-boundary correspondence of (1+1)D symmetric gapped phases
An operator-algebraic framework proves that boundary conditions in (1+1)D gapped phases with categorical symmetry are classified by objects of the module category M_Q^op via an equivalence of categories, yielding a bulk-boundary correspondence as the enriched center.
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Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions
Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.