English

Vassiliev knot invariants and Chern-Simons perturbation theory to all orders

q-alg 2009-10-30 v2 Quantum Algebra

Abstract

At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot invariants. Moreover these are finite type invariants whose order coincides with the order in the perturbative expansion. Together they combine to give a universal Vassiliev invariant.

Keywords

Cite

@article{arxiv.q-alg/9603010,
  title  = {Vassiliev knot invariants and Chern-Simons perturbation theory to all orders},
  author = {Daniel Altschuler and Laurent Freidel},
  journal= {arXiv preprint arXiv:q-alg/9603010},
  year   = {2009}
}

Comments

Revised version, includes a detailed proof of formula (5.26) for $\log Z$, and several minor changes. 31 pages, 19 figures, epsf.sty, LateX