The Generating Functional of the Kontsevich Integral and its Derivation as a Holonomy

TL;DR

This paper introduces an algebra bundle with a Knizhnik-Zamolodchikov connection over configuration spaces, demonstrating that its holonomy generates the Kontsevich integral for braids, linking algebraic and topological structures.

Contribution

It constructs a novel algebra bundle and establishes a direct link between holonomy of a specific connection and the Kontsevich integral for braids.

Findings

Holonomy of the KZ connection generates the Kontsevich integral.

Algebra bundle of chord diagrams over configuration space is introduced.

Provides a geometric interpretation of the Kontsevich integral.

Abstract

We introduce an algebra bundle of chord diagrams over the configuration space of N points in the complex plane on which we put the Knizhnik-Zamolodchikov connection. For that particular connection, the holonomy along a loop in the base is shown to be generating the Kontsevich integral for that loop's associated braid.