Reshetikhin-Turaev TQFTs close under generalised orbifolds

We specialise the construction of orbifold graph TQFTs introduced in Carqueville et al., arXiv:2101.02482 to Reshetikhin-Turaev defect TQFTs. We explain that the modular fusion category \({\mathcal{C}}_{\mathcal{A}}\) constructed in Mulevičius-Runkel, arXiv:2002.00663 from an orbifold datum \(\mathc...

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Bibliographic Details
Published inarXiv.org
Main Authors Carqueville, Nils, Mulevicius, Vincentas, Runkel, Ingo, Schaumann, Gregor, Scherl, Daniel
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.09.2021
Subjects
Algebra
Categories
Modular construction
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Summary:We specialise the construction of orbifold graph TQFTs introduced in Carqueville et al., arXiv:2101.02482 to Reshetikhin-Turaev defect TQFTs. We explain that the modular fusion category \({\mathcal{C}}_{\mathcal{A}}\) constructed in Mulevičius-Runkel, arXiv:2002.00663 from an orbifold datum \(\mathcal{A}\) in a given modular fusion category \(\mathcal{C}\) is a special case of the Wilson line ribbon categories introduced as part of the general theory of orbifold graph TQFTs. Using this, we prove that the Reshetikhin-Turaev TQFT obtained from \({\mathcal{C}}_{\mathcal{A}}\) is equivalent to the orbifold of the TQFT for \(\mathcal{C}\) with respect to the orbifold datum \(\mathcal{A}\).
ISSN:2331-8422