Constructing modular categories from orbifold data

Abstract

The notion of an orbifold datum A in a modular fusion category C 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 C, we introduce a ribbon category CA and show that it is again a modular fusion category. The definition of CA 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 ∆-separable Frobenius algebra A in C; (ii) when A is an orbifold datum in C D Vect, built from a spherical fusion category S. We show that, in case (i), CA is ribbon-equivalent to the category of local modules of A, and, in case (ii), to the Drinfeld centre of S. The category CA thus unifies these two constructions into a single algebraic setting.