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Category theory for conformal boundary conditions
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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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Cited by 3 Pith papers
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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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Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
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Categorified structures over moduli spaces: Anomalies, non-invertible symmetries, and exceptional holonomy
The paper conjectures that non-invertible Ising and tricritical Ising symmetries organize closed string states and D-brane categories into categorical bundles over moduli spaces of exceptional holonomy compactifications.
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