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

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

1993-05-08

arxiv.org/abs/hep-th/9305032v1

Commun.Math.Phys. 162 (1994) 289-320

Physics

High Energy Physics

High Energy Physics - Theory

48 pages + 20 diagrams

Scientific paper

10.1007/BF02102019

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.

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