Perturbative and Non-perturbative Aspects of the Chern-Simons-Witten Theory

Abstract

We investigate a relation between non-perturbative and perturbative cases in the 2+1 dimensional Chern-Simons-Witten (CSW) theory for G = E₆ gauge group. In the perturbative case, we calculate the vacuum expectation value (VEV) of an unknotted Wilson loop operator up to order 1/k³ (k is a coupling constant). The result above is proved to be identical to the polynomial invariant E0 (ρ) in the non-perturbative case at the same order of expansion.