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- Title
Constructing modular categories from orbifold data.
- Authors
Mulevičius, Vincentas; Runkel, Ingo
- Abstract
The notion of an orbifold datum A in a modular fusion category ... was introduced as part of a generalised orbifold construction for Reshetikhin–Turaev TQFTs by Carqueville, Runkel, and Schaumann in 2018. In this paper, given a simple orbifold datum A in ..., we introduce a ribbon category ...A and show that it is again a modular fusion category. The definition of ...A is motivated by properties of Wilson lines in the generalised orbifold. We analyse two examples in detail: (i) when A is given by a simple commutative Δ-separable Frobenius algebra A in ...; (ii) when A is an orbifold datum in ... = Vect, built from a spherical fusion category S. We show that, in case (i), ...A is ribbon-equivalent to the category of local modules of A, and, in case (ii), to the Drinfeld centre of S. The category ...A thus unifies these two constructions into a single algebraic setting.
- Subjects
ORBIFOLDS; FROBENIUS algebras; TOPOLOGICAL fields
- Publication
Quantum Topology, 2022, Vol 13, Issue 3, p459
- ISSN
1663-487X
- Publication type
Article
- DOI
10.4171/QT/170