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

Asep Yoyo Wardaya (1) Department of Physics, Diponegoro University, Semarang 2) Indonesia Center for Theoretical and Mathematical Physics)
Freddy P. Zen (1) Indonesia Center for Theoretical and Mathematical Physics. 2) Theoretical Physics Laboratory, Institut Teknologi Bandung, Bandung)
Jusak S Kosasih (1) Indonesia Center for Theoretical and Mathematical Physics. 2) Theoretical Physics Laboratory, Institut Teknologi Bandung, Bandung)
Triyanta Triyanta (1) Indonesia Center for Theoretical and Mathematical Physics. 2) Theoretical Physics Laboratory, Institut Teknologi Bandung, Bandung)

Indonesian Journal of Physics (IJP)
Vol 19 No 1 (2008): Vol. 19 No. 1, January 2008

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.