Chern-simons theories, wilson lines and conformal blocks

Abstract

We consider the Chern-Simons theory of a gauge group SU(N) and meaning of Wilson line on three dimensional manifold. On $D \times R,\; T^2\times R$ the C-S theory is equivalent to WZW model and we see the phase space of C-S theory. We show that by using operator formalism on $S^3$ Hilbert space of the C-S theory is equivalent to the conformal blocks of CFT and by using the monodromy properties of conformal blocks explicitly calculate the expectation value of the Wilson lines for SU(N) with fundamental representation.