Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory
Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory
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从共形场理论构建 Witten-Reshetikhin-Turaev TQFT
DOI：
10.1007/s00222-014-0555-7
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Juergen E. Andersen & Kenji Ueno
中科院分区：
文献类型：
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作者：
Tomonari Doteral;Masakiyo Kimoto;Junichi Matsuzawa;Akira Ishii;Yoshifumi Tsuchimoto;Akira Ishii;Akira Ishii;石井亮;Yoshifumi Tsuchimoto;土基 善文;松澤 淳一;菊地 克彦;石井 亮;Takuro Mochizuki;石井亮;Takuro Mochizuki;土基 善文;Akira Ishii;Yoshifumi Tsuchimoto;石井亮;Takuro Mochizuki;Takuro Mochizuki;Takuro Mochizuki;Takuro Mochizuki;Juergen E. Andersen & Kenji Ueno
在Andersen和Ueno(J Knot They Ramif 16：127-202,2007)中，我们在Tuchiya等人发展的真空束理论的基础上构造了真空模函子。(ADV Stud Pure Math 19：459-566,1989)和Andersen和Ueno中的阿贝尔模拟(Int J Math 18：919-993,2007)。在这里，我们提供了Blanchet，Habbeer，Masbaum和Vogel的Witten-Reshetikhin-Turaev TQFT的Skein理论模型下的模函数到Vacua模函数的显式同构。因此，这提供了TQFT的几何结构，该几何结构首先由Witten提出，并由Reshetikhin-Turaev首先从量子群构造。
In Andersen and Ueno (J Knot Theory Ramif 16:127–202, 2007) we constructed thevacua modular functorbased 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.