The volume conjecture and topological strings
Abstract
In this paper, we discuss a relation between Jones-Witten theory of knot invariants and topological open string theory on the basis of the volume conjecture. We find a similar Hamiltonian structure for both theories, and interpret the AJ conjecture as the D-module structure for a D-brane partition function. In order to verify our claim, we compute the free energy for the annulus contributions in the topological string using the Chern-Simons matrix model, and find that it coincides with the Reidemeister torsion in the case of the figure-eight knot complement and the SnapPea census manifold m009.
- Publication:
-
Fortschritte der Physik
- Pub Date:
- September 2009
- DOI:
- 10.1002/prop.200900067
- arXiv:
- arXiv:0903.2084
- Bibcode:
- 2009ForPh..57..825D
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- 52 pages, 10 figures, references added, typos corrected, comments included