Analysis of Observables in Chern-Simons Perturbation Theory

TL;DR

This paper investigates Chern-Simons theory with gauge group SU(N) using perturbation theory, computing knot invariants up to order g^6 and confirming theoretical predictions about quantum corrections and framing dependence.

Contribution

It provides a perturbative analysis of knot observables in Chern-Simons theory, confirming Witten's predictions about framing dependence and quantum corrections at two loops.

Findings

Vacuum expectation value of the unknot computed up to order g^6.

No quantum correction at two loops for the two-point function.

Framing dependence factorizes as predicted by Witten.

Abstract

Chern-Simons Theory with gauge group $SU(N)$ is analyzed from a perturbation theory point of view. The vacuum expectation value of the unknot is computed up to order $g^6$ and it is shown that agreement with the exact result by Witten implies no quantum correction at two loops for the two-point function. In addition, it is shown from a perturbation theory point of view that the framing dependence of the vacuum expectation value of an arbitrary knot factorizes in the form predicted by Witten.