BIMSA >
YMSC-BIMSA Quantum Information Seminar
YMSC-BIMSA Quantum Information Seminar
Abelian Chern–Simons Theory = Reshetikhin–Turaev Theory
Abelian Chern–Simons Theory = Reshetikhin–Turaev Theory
Organizers
Speaker
Daniel Galviz
Time
Friday, April 10, 2026 4:00 PM - 5:30 PM
Venue
Shuangqing-B626
Online
Zoom 230 432 7880
(BIMSA)
Abstract
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.