Classification of 2D fermionic systems with Z2 flavor symmetry yields 16 consistent superfusion categories labeled by anomaly invariants (ν_W, ν_Z, ν_WZ).
Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
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abstract
We construct the $Z_{N}$ symmetry extended fusion ring of bulk and chiral theories and the corresponding modular partition functions with nonanomalous subgroup $Z_{n}(\subset Z_{N})$. The chiral fusion ring provides fundamental data for $Z_{N}$- graded symmetry topological field theories and also provides algebraic data for smeared boundary conformal field theories, which describe the zero modes of the extended models. For more general multicomponent or coupled systems, we also obtain a new series of extended theories. By applying the folding trick, their partition functions correspond to charged or gapped domain walls or massless renormalization group flows preserving quotient group structures.
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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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Classification of 2D Fermionic Systems with a $\mathbb Z_2$ Flavor Symmetry
Classification of 2D fermionic systems with Z2 flavor symmetry yields 16 consistent superfusion categories labeled by anomaly invariants (ν_W, ν_Z, ν_WZ).
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
- Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries