Chern-Simons Invariants of Torus Links
arXiv:1003.2861 · doi:10.1007/s00023-010-0058-z
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.
20 pages, 5 figures; v2: minor changes, version submitted to AHP. The final publication is available at http://www.springerlink.com/content/a2614232873l76h6/