Constructing modular categories from orbifold data
Vincentas Mulevičius
Universität Hamburg, GermanyIngo Runkel
Universität Hamburg, Germany
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Abstract
The notion of an orbifold datum 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 in , we introduce a ribbon category and show that it is again a modular fusion category. The definition of is motivated by properties of Wilson lines in the generalised orbifold. We analyse two examples in detail: (i) when is given by a simple commutative -separable Frobenius algebra in ; (ii) when is an orbifold datum in , built from a spherical fusion category . We show that, in case (i), is ribbon-equivalent to the category of local modules of , and, in case (ii), to the Drinfeld centre of . The category thus unifies these two constructions into a single algebraic setting.
Cite this article
Vincentas Mulevičius, Ingo Runkel, Constructing modular categories from orbifold data. Quantum Topol. 13 (2022), no. 3, pp. 459–523
DOI 10.4171/QT/170