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Generalized Cardy conditions of topological defect lines
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abstract
We propose a systematic procedure to work out systems of topological defect lines (TDLs) in minimal models. The only input of this method is the modular invariant partition function. For diagonal and permutation diagonal models, we prove there is a bijection between simple TDLs and primary fields preserving fusion rules. For block-diagonal models, we work out simple TDLs in the $3$-state Potts model as an example. The results agree with those in $3D$ topological field theory methods.
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ADE triality via (non-)invertible symmetry gauging
Gauging a non-invertible symmetry exchanges the D7 and E6 minimal models, completing the ADE triality.
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