Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Anomalies of coset non-invertible symmetries
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Gauging anomalous onsite symmetries in LSM-anomalous spin chains yields a noninvertible crystalline categorical symmetry whose breaking transitions correspond to the original DQCPs, realized as Rep(D8) and Rep(H8) categorical Landau transitions.
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra, enabling braiding computations in the 3D SymTFT.
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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Understanding deconfined quantum critical points from crystalline categorical Landau paradigm
Gauging anomalous onsite symmetries in LSM-anomalous spin chains yields a noninvertible crystalline categorical symmetry whose breaking transitions correspond to the original DQCPs, realized as Rep(D8) and Rep(H8) categorical Landau transitions.