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

• 成果类型: Article
• 署名作者: Andersen, Jorgen Ellegaard; Ueno, Kenji
• 署名单位: Aarhus University; Hosei University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0555-7
• 发表日期: 2015
• 页码: 519-559
• 关键词: nielsen-thurston classification; mapping class-groups; 3-manifold invariants; hecke algebras; modular categories; su(n) invariants; kauffman bracket; link polynomials; quantum groups; REPRESENTATIONS

摘要

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 .