Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Fukusumi,Composing parafermions: a construction ofZ N fractional quantum Hall systems and a modern understanding of confinement and duality,2212.12999
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Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.