Non-invertible so(3)_k defect lines that commute with the massless perturbation of N=2 minimal models are killed at second order by a supersymmetry anomaly, while the Chebyshev massive deformation preserves them to all orders.
Bulk perturbations of N=2 branes
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The evolution of supersymmetric A-type D-branes under the bulk renormalization group flow between two different N=2 minimal models is studied. Using the Landau-Ginzburg description we show that a specific set of branes decouples from the infrared theory, and we make detailed predictions for the behavior of the remaining branes. The Landau-Ginzburg picture is then checked against a direct conformal field theory analysis. In particular we construct a natural index pairing which is preserved by the RG flow, and show that the branes that decouple have vanishing index with the surviving branes.
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$\mathcal{N}=2$ RG flows, Non-Invertible Symmetries and Matrix Factorisations
Non-invertible so(3)_k defect lines that commute with the massless perturbation of N=2 minimal models are killed at second order by a supersymmetry anomaly, while the Chebyshev massive deformation preserves them to all orders.