Orbifolds of Reshetikhin-Turaev TQFTs

Abstract

We construct three classes of generalised orbifolds of Reshetikhin-Turaev theory for a modular tensor category $\mathcal{C}$, using the language of defect TQFT from [arXiv:1705.06085]: (i) spherical fusion categories give orbifolds for the "trivial" defect TQFT associated to vect, (ii) $G$-crossed extensions of $\mathcal{C}$ give group orbifolds for any finite group $G$, and (iii) we construct orbifolds from commutative $\Delta$-separable symmetric Frobenius algebras in $\mathcal{C}$. We also explain how the Turaev-Viro state sum construction fits into our framework by proving that it is isomorphic to the orbifold of case (i). Moreover, we treat the cases (ii) and (iii) in the more general setting of ribbon tensor categories. For case (ii) we show how Morita equivalence leads to isomorphic orbifolds, and we discuss Tambara-Yamagami categories as particular examples.

51 pages; v2: minor improvements and slightly extended exposition

References in corpus (4)

• Orbifolds of n-dimensional defect TQFTs
• Discrete torsion defects
• 3-dimensional defect TQFTs and their tricategories
• Line and surface defects in Reshetikhin-Turaev TQFT

Cited by in corpus (8)

• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• On lattice models of gapped phases with fusion category symmetries
• Orbifolds of n-dimensional defect TQFTs
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Line and surface defects in Reshetikhin-Turaev TQFT
• Condensations in higher categories
• Domain walls between 3d phases of Reshetikhin-Turaev TQFTs
• Orbifold graph TQFTs