A Stringy Generalization of the Kontsevich Integral

TL;DR

This paper introduces a generalized version of the Kontsevich integral that extends to graphs in three-dimensional space, providing a new perspective on knot invariants and their geometric interpretations.

Contribution

It presents a minimal Kontsevich integral that generates the original and extends the definition to graphs in R^3, exploring their interactions and boundary behaviors.

Findings

Defines a minimal Kontsevich integral generating the original

Extends the integral to graphs in three-dimensional space

Analyzes the behavior of graph interactions in the generalized framework

Abstract

We introduce a "minimal" Kontsevich integral that generates the original Kontsevich integral while at the same time producing ribbons whose boundaries are the braids on which the minimal Kontsevich integral is evaluated. We generalize the definition of the Kontsevich integral to that of graphs in R^3 and study the behavior of such expressions as different graphs are brought together, thus leading to a 2-dimensional generalization of the Kontsevich integral.