Vassiliev Invariants for Links from Chern-Simons Perturbation Theory

Details Vassiliev Invariants for Links from Chern-Simons Perturbation Theory Vassiliev Invariants for Links from Chern-Simons Perturbation Theory

1996-07-03

arxiv.org/abs/hep-th/9607030v1

Nucl.Phys. B488 (1997) 677-718

Physics

High Energy Physics

High Energy Physics - Theory

44 pages, LaTex, epsf.sty, 15 figures

Scientific paper

10.1016/S0550-3213(96)00689-X

The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel the algebraic structure encoded in the group factors of the perturbative series expansion. In the process a factorization theorem is proved for Wilson lines. Wilson lines are then closed back into Wilson loops and new link invariants of finite type are defined. Integral expressions for these invariants are presented for the first three primitive ones of lower degree in the case of two-component links. In addition, explicit numerical results are obtained for all two-component links of no more than six crossings up to degree four.

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