Reshetikhin–Turaev TQFTs Close Under Generalised Orbifolds

Abstract We specialise the construction of orbifold graph TQFTs introduced in Carqueville et al. (Orbifold graph TQFTs) to Reshetikhin–Turaev defect TQFTs. We explain that the modular fusion category $$\mathcal {C}_\mathcal {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:math> constructed in Mulevičius and Runkel (Quant Topol 13(3):459–523, 2023. https://doi.org/10.4171/QT/170 ) from an orbifold datum $$\mathcal {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> in a given modular fusion category $$\mathcal {C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> 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 $$\mathcal {C}_\mathcal {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:math> is equivalent to the orbifold of the TQFT for $$\mathcal {C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> with respect to the orbifold datum $$\mathcal {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> .