Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left-right symmetries and boundary conditions in 2D CFTs.
Gauging Non-Invertible Symmetries in (2+1)d Topological Orders,
5 Pith papers cite this work. Polarity classification is still indexing.
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Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, and holographic Romans mass setups.
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
Framework using smeared boundary CFTs classifies gapped phases dual to massless RG flows, showing they often spontaneously break non-group-like symmetries via unusual module structures outside standard boundary critical phenomena.
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Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.