RG domain walls between Z_N parafermions and minimal models support a continuous defect conformal manifold generated by a spin-1 phantom current, with transmission rate vanishing at large N.
Category theory for conformal boundary conditions
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abstract
We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a by-product we obtain results about the Frobenius-Schur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity. We apply our results to the description of boundary conditions in two-dimensional conformal field theory and present illustrative examples. We show that when the module category is tensor, then it gives rise to a NIM-rep of the fusion rules, and discuss a possible relation with the representation theory of vertex operator algebras.
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Defect Conformal Manifolds along RG Domain Walls between $\mathbb Z_N$-Parafermions and Minimal Models
RG domain walls between Z_N parafermions and minimal models support a continuous defect conformal manifold generated by a spin-1 phantom current, with transmission rate vanishing at large N.
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