Chern-Simons Theory, Colored-Oriented Braids and Link invariants

Abstract

A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for the correlators of $SU(2)_k$ Wess-Zumino conformal field theory are presented. A large class of representations of the generators of the groupoid of coloured-oriented braids are obtained. These provide a whole lot of new link invariants of which Jones polynomials are the simplest examples. These new invariants are explicitly calculated as illustrations for knots upto eight crossings and two-component multicoloured links upto seven crossings.