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.
On the boundary coupling of topological Landau-Ginzburg models
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I propose a general form for the boundary coupling of B-type topological Landau-Ginzburg models. In particular, I show that the relevant background in the open string sector is a (generally non-Abelian) superconnection of type (0,1) living in a complex superbundle defined on the target space, which I allow to be a non-compact Calabi-Yau manifold. This extends and clarifies previous proposals. Generalizing an argument due to Witten, I show that BRST invariance of the partition function on the worldsheet amounts to the condition that the (0,<= 2) part of the superconnection's curvature equals a constant endomorphism plus the Landau-Ginzburg potential times the identity section of the underlying superbundle. This provides the target space equations of motion for the open topological model.
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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.