Pointed Drinfeld center functor

Abstract

In this work, using the functoriality of Drinfeld center of fusion categories, we generalize an earlier result on the functoriality of full center of simple separable algebras in a fixed fusion category to all fusion categories. This generalization produces a new center functor, which involves both Drinfeld center and full center and will be called the pointed Drinfeld center functor. We prove that this pointed Drinfeld center functor is a symmetric monoidal equivalence. It turns out that this functor provides a precise and rather complete mathematical formulation of the boundary-bulk relation of 1+1D rational conformal field theories (RCFT). In this process, we solve an old problem of computing the fusion of two 0D (or 1D) wall CFT's along a non-trivial 1+1D bulk RCFT.

arXiv comment34 pages, 8 figures, comments are welcome

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Cited by in corpus (10)

• Classification of topological phases with finite internal symmetries in all dimensions
• A mathematical theory of gapless edges of 2d topological orders. Part I
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• A mathematical theory of gapless edges of 2d topological orders. Part II
• Categories of quantum liquids I
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Categories of quantum liquids II
• Enriched monoidal categories I: centers
• Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries
• Separable algebras in multitensor C${}^{\ast }$-categories are unitarizable