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Constructing modular categories from orbifold data | | Vincentas Mulevicius
; Ingo Runkel
; | | Date: |
3 Feb 2020 | | Abstract: | 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. | | Source: | arXiv, 2002.0663 | | Services: | Forum | Review | PDF | Favorites | |
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