Constructing modular categories from orbifold data

In Carqueville et al., arXiv:1809.01483, the notion of an orbifold datum $mathbb{A}$ in a modular fusion category $mathcal{C}$ was introduced as part of a generalised orbifold construction for Reshetikhin-Turaev TQFTs. In this paper, given a simple orbifold datum $mathbb{A}$ in $mathcal{C}$, we introduce a ribbon category $mathcal{C}_{mathbb{A}}$ and show that it is again a modular fusion category. The definition of $mathcal{C}_{mathbb{A}}$ is motivated by properties of Wilson lines in the generalised orbifold. We analyse two examples in detail: (i) when $mathbb{A}$ is given by a simple commutative $Delta$-separable Frobenius algebra $A$ in $mathcal{C}$; (ii) when $mathbb{A}$ is an orbifold datum in $mathcal{C} = operatorname{Vect}$, built from a spherical fusion category $mathcal{S}$. We show that in case (i), $mathcal{C}_{mathbb{A}}$ is ribbon-equivalent to the category of local modules of $A$, and in case (ii), to the Drinfeld centre of $mathcal{S}$. The category $mathcal{C}_{mathbb{A}}$ thus unifies these two constructions into a single algebraic setting.