Perturbative Chern–Simons theory from the Penner model

Abstract

We show explicitly that the perturbative SU(N) Chern–Simons theory arises naturally from two Penner models, with opposite coupling constants. As a result computations in the perturbative Chern–Simons theory are carried out using the Penner model, and it turns out to be simpler and transparent. It is also shown that the connected correlators of the puncture operator in the Penner model are related to the connected correlators of the operator that gives the Wilson loop operator in the conjugacy class.