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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.
We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on the $W$-matrix--the quantum invariant of a colored framed Whitehead link
A generalised orbifold of a defect TQFT $mathcal{Z}$ is another TQFT $mathcal{Z}_{mathcal{A}}$ obtained by performing a state sum construction internal to $mathcal{Z}$. As an input it needs a so-called orbifold datum $mathcal{A}$ which is used to lab
Using M-theory in physics, Cho, Gang, and Kim (JHEP 2020, 115 (2020) ) recently outlined a program that connects two parallel subjects of three dimensional manifolds, namely, geometric topology and quantum topology. They suggest that classical topolo
We investigate the kernel space of an integral operator M(g) depending on the spin g and describing an elliptic Fourier transformation. The operator M(g) is an intertwiner for the elliptic modular double formed from a pair of Sklyanin algebras with t
The definitions of the $n^{th}$ Gauss sum and the associated $n^{th}$ central charge are introduced for premodular categories $mathcal{C}$ and $ninmathbb{Z}$. We first derive an expression of the $n^{th}$ Gauss sum of a modular category $mathcal{C}$,