Knot invariants and universal R-matrices from perturbative Chern-Simons theory in the almost axial gauge

Abstract

Using perturbative Chern-Simons theory in the almost axial gauge on the euclidean manifold S 1 × R 2, we give a prescription for the computation of knot invariants. The method gives the correct expectation value of the unknot to all orders in perturbation theory and gives the correct answer for the spectral-parameter-dependent universal R-matrix to second order. All results are derived for a general semi-simple Lie algebra.