The R-matrix in 3d topological BF theory

Abstract

In this paper, I study Wilson line operators in a certain type of “split” Chern–Simons theory for a Lie-algebra \(\mathfrak {g}={\mathfrak {a}}\oplus {\mathfrak {a}}^*\) on a manifold with boundaries. The resulting gauge theory is a 3d topological BF theory equivalent to a topologically twisted 3d \({\mathcal {N}}=4\) theory. I show that this theory realises solutions to the quantum Yang–Baxter equation all orders in perturbation theory as the expectation value of crossing Wilson lines.