An analytic Approach to Turaev's Shadow Invariant
Mathematical Physics
2011-12-20 v7 High Energy Physics - Theory
math.MP
Abstract
In the present paper we extend the "torus gauge fixing approach" by Blau and Thompson (Nucl. Phys. B408(1):345--390, 1993) for Chern-Simons models with base manifolds M of the form M= \Sigma x S^1 in a suitable way. We arrive at a heuristic path integral formula for the Wilson loop observables associated to general links in M. We then show that the right-hand side of this formula can be evaluated explicitly in a non-perturbative way and that this evaluation naturally leads to the face models in terms of which Turaev's shadow invariant is defined.
Keywords
Cite
@article{arxiv.math-ph/0507040,
title = {An analytic Approach to Turaev's Shadow Invariant},
author = {Atle Hahn},
journal= {arXiv preprint arXiv:math-ph/0507040},
year = {2011}
}
Comments
44 pages, 2 figures. Changes have been made in Sec. 2.3, Sec 2.4, Sec. 3.4, and Sec. 3.5. Appendix C is new