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Chern-Simons invariants of torus links. (English) Zbl 1208.81149
Summary: We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus knots and links, and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
58J28 Eta-invariants, Chern-Simons invariants
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
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