A Wilson Line Realisation of Quantum Groups

2023/07/20 by Nanna Havn Aamand, Aamand, Nanna, Dani Kaufman +1
Mathematics · Physics and Astronomy · #57K16 (Primary) 17B37 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2307.10830

openalex publication_date 2023/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The study of this paper is Wilson line operators in 3-dimensional Chern-Simons theory on a manifold with boundaries. We 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 U_h(\mathfrak g). We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.

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