Geodesic
Orbifolds of Reshetikhin-Turaev TQFTs
Theory and applications of categories, Tome 35 (2020), pp. 513-561.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We construct three classes of generalised orbifolds of Reshetikhin-Turaev theory for a modular tensor category C, using the language of defect TQFT: (i) spherical fusion categories give orbifolds for the "trivial" defect TQFT associated to Vect, (ii) G-crossed extensions of C give group orbifolds for any finite group G, and (iii) we construct orbifolds from commutative Δ-separable Frobenius algebras in 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.
Publié le :
Classification : 57K16, 18M20, 57R56
Keywords: topological quantum field theory, orbifold construction, Reshetikhin-Turaev theory, modular tensor categories 
@article{TAC_2020_35_a14,
     author = {Nils Carqueville and Ingo Runkel and Gregor Schaumann},
     title = {Orbifolds of {Reshetikhin-Turaev} {TQFTs}},
     journal = {Theory and applications of categories},
     pages = {513--561},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a14/}
}
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Nils Carqueville; Ingo Runkel; Gregor Schaumann. Orbifolds of Reshetikhin-Turaev TQFTs. Theory and applications of categories, Tome 35 (2020), pp. 513-561. http://geodesic.mathdoc.fr/item/TAC_2020_35_a14/