Three Dimensional Chern-Simons Theory as a Theory of Knots and Links

TL;DR

This paper explores three-dimensional SU(2) Chern-Simons theory as a topological field theory for knots and links, developing a systematic method to derive link invariants including Jones polynomials.

Contribution

It introduces a new systematic approach within Chern-Simons theory to compute knot and link invariants, expanding the toolkit for topological quantum field theory applications.

Findings

Developed a method to obtain link invariants from Chern-Simons theory.

Connected conformal field theory monodromy to knot invariants.

Produced new knot invariants beyond Jones polynomials.

Abstract

Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants within this field theoretic framework. The monodromy properties of the correlators of the associated Wess-Zumino SU(2)$_k$ conformal field theory on a two-dimensional sphere prove to be useful tools. The method is simple enough to yield a whole variety of new knot invariants of which the Jones polynomials are the simplest example.