Three Dimensional Chern-Simons Theory as a Theory of Knots and Links III : Compact Semi-simple Group

TL;DR

This paper extends the application of Chern-Simons theory to knots and links by developing a method for invariants involving up to four-strand braids, generalizing previous SU(2) results.

Contribution

It introduces a new technique to compute link invariants for a broader class of gauge groups within Chern-Simons theory.

Findings

Developed a method for invariants of links with up to four strands

Generalized previous SU(2) Chern-Simons knot invariants

Enhanced understanding of non-abelian gauge group applications

Abstract

Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This generalizes our earlier work on $SU(2)$ Chern-Simons theory.