Kontsevich Integral for Vassiliev Invariants from Chern-Simons Perturbation Theory in the Light-Cone Gauge

TL;DR

This paper explores the perturbative series expansion of Chern-Simons gauge theory in the light-cone gauge, revealing its connection to the Kontsevich integral and Vassiliev invariants of framed knots, aligning with non-perturbative results.

Contribution

It demonstrates that the perturbative expansion in the light-cone gauge reproduces the Kontsevich integral for Vassiliev invariants, incorporating framing dependence consistent with other methods.

Findings

Perturbative series matches non-perturbative framing dependence.

The Kontsevich integral naturally appears in the light-cone gauge analysis.

Framing effects are consistent across different computational approaches.

Abstract

We analyse the structure of the perturbative series expansion of Chern-Simons gauge theory in the light-cone gauge. After introducing a regularization prescription that entails the consideration of framed knots, we present the general form of the vacuum expectation value of a Wilson loop. The resulting expression turns out to give the same framing dependence as the one obtained using non-perturbative methods and perturbative methods in covariant gauges. It also contains the Kontsevich integral for Vassiliev invariants of framed knots.