Inventiones mathematicae

, Volume 201, Issue 2, pp 519–559 | Cite as

Construction of the Witten–Reshetikhin–Turaev TQFT from conformal field theory



In Andersen and Ueno (J Knot Theory Ramif 16:127–202, 2007) we constructed the vacua modular functor based on the sheaf of vacua theory developed in Tsuchiya et al. (Adv Stud Pure Math 19:459–566, 1989) and the abelian analog in Andersen and Ueno (Int J Math 18:919–993, 2007). We here provide an explicit isomorphism from the modular functor underlying the skein-theoretic model for the Witten–Reshetikhin–Turaev TQFT due to Blanchet, Habbeger, Masbaum and Vogel to the vacua modular functor. This thus provides a geometric construction of the TQFT first proposed by Witten and constructed first by Reshetikhin–Turaev from the quantum group \(U_q(\text{ sl }(N))\).



We thank Christian Blanchet, Yukihiro Kanie, Gregor Masbaum, Akihiro Tsuchiya and Yasuhiko Yamada for valuable discussions and the referee for several helpful comments which improved the paper.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Center for Quantum Geometry of Moduli SpacesUniversity of AarhusAarhusDenmark
  2. 2.Faculty of Science and Engineering, Department of Industrial and System EngineeringHosei UniversityKoganeiJapan

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