CHERN-SIMONS THEORY AND KAUFFMAN POLYNOMIALS

Abstract

We report on a study of the expectation values of Wilson loops in D=3 Chern-Simons theory. The general skein relations (of higher orders) are derived for these expectation values. We show that the skein relations for the Wilson loops carrying the fundamental representations of the simple Lie algebras SO(n) and Sp(n) are sufficient to determine invariants for all knots and links and that the resulting link invariants agree with Kauffman polynomials. The polynomial for an unknotted circle is identified to the formal characters of the fundamental representations of these Lie algebras.