An analytic Approach to Turaev's Shadow Invariant
arXiv:math-ph/0507040 · doi:10.1142/S021821650800666X
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= Σx 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.
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
References in corpus (5)
- Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
- A Note on Knot Invariants and q-Deformed 2d Yang-Mills
- Variational Bounds for the Generalized Random Energy Model
- From simplicial Chern-Simons theory to the shadow invariant I
- From simplicial Chern-Simons theory to the shadow invariant II