Orbifolds of ReshetikhinTuraev TQFTs
Abstract
We construct three classes of generalised orbifolds of ReshetikhinTuraev 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 TuraevViro 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 TambaraYamagami categories as particular examples.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.01483
 Bibcode:
 2018arXiv180901483C
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 51 pages