TL;DR
This paper computes Chern-Simons invariants for torus links, providing explicit formulas for various gauge groups and representations, and tests a conjecture relating HOMFLY and Kauffman invariants.
Contribution
It introduces explicit formulas for invariants of torus links in Chern-Simons theory for all classical gauge groups and representations, including new results for Kauffman invariants and cable knots.
Findings
Reproduces known HOMFLY invariants for torus links
Derives new formulas for Kauffman invariants
Tests a conjecture relating HOMFLY and Kauffman invariants
Abstract
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 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.
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