A Wilson line realization of quantum groups

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 \(U_\hbar ({\mathfrak {g}})\) $U_{ħ}(\mathfrak{g})$ . We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.