Tetrahedron Diagram and Perturbative Calculation in Chern-Simons-Witten Theory

We investigate extended Wilson loop operators, in particular tetrahedron operator in (2 + 1)-dimensional Chern-Simons-Witten theory. This operator emerges naturally from the contribution terms in twoparticle scattering amplitude. We evaluate this diagram non-perturbatively in terms of vacuum expectation values of Wilson loop operators, especially for gauge group SU(N) with specific choices of representations. On the other hand, we also discuss the perturbative calculation of vacuum expectation value in this theory. We show that, up to the third order, this values of unknotted Wilson loop operators are identical to the non-perturbative result.