Perturbative Chern-Simons Theory From The Penner Model

TL;DR

This paper demonstrates how perturbative SU(N) Chern-Simons theory can be derived from two Penner models, simplifying calculations and revealing connections between correlators of puncture and Wilson loop operators.

Contribution

It explicitly establishes the emergence of perturbative Chern-Simons theory from Penner models with opposite couplings, providing a new computational approach.

Findings

Chern-Simons theory derived from Penner models

Simplified computation of perturbative Chern-Simons

Relation between puncture and Wilson loop correlators

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.