A Wilson line realization of quantum groups

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We study Wilson line operators in three-dimensional Chern–Simons theory on a manifold with boundaries and prove to leading order, through a direct calculation of Feynman integrals, that the merging of parallel Wilson lines reproduces the coproduct on the quantum group Uħ(g) . We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.

Original languageEnglish
Article number12
JournalLetters in Mathematical Physics
Issue number1
Number of pages19
Publication statusPublished - 2024

Bibliographical note

Funding Information:
The authors were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 772960), and the Copenhagen Centre for Geometry and Topology (DNRF151). Our special thanks goes to Kevin Costello, Nathalie Wahl and Ryszard Nest for helpful suggestions and discussions.

Publisher Copyright:
© 2024, The Author(s).

    Research areas

  • 17B37, 57K16, Chern–Simons theory, Perturbation theory, Primary: 81T45, Quantum group, Secondary: 81T15, Wilson line

ID: 390513437