Abelian Chern–Simons Theory = Reshetikhin–Turaev Theory
演讲者
Daniel Galviz
时间
2026年04月10日 16:00 至 17:30
地点
Shuangqing-B626
线上
Zoom 230 432 7880
(BIMSA)
摘要
Chern–Simons theory and Reshetikhin–Turaev theory were introduced decades ago and are expected to define the same topological quantum field theory. While this remains conjectural in the non-Abelian case, in the Abelian case we prove that they are indeed the same extended 3-dimensional topological quantum field theory. In this talk, I will explain the main ideas in the $U(1)$ case.
For higher-rank Abelian theories, we develop new tools for the geometric quantization of $U(1)^n$ Chern–Simons theory and establish an isomorphism with the corresponding Reshetikhin–Turaev theory as an extended TQFT. As a consequence, Abelian Chern–Simons theories are classified by finite quadratic modules. If time allows, I will also explain how this leads to a mathematical derivation of the data $(S, T, c)$ underlying 2+1D bosonic topological orders in Xiao-Gang Wen’s framework.
For higher-rank Abelian theories, we develop new tools for the geometric quantization of $U(1)^n$ Chern–Simons theory and establish an isomorphism with the corresponding Reshetikhin–Turaev theory as an extended TQFT. As a consequence, Abelian Chern–Simons theories are classified by finite quadratic modules. If time allows, I will also explain how this leads to a mathematical derivation of the data $(S, T, c)$ underlying 2+1D bosonic topological orders in Xiao-Gang Wen’s framework.