The Volume Conjecture and Topological Strings

Details The Volume Conjecture and Topological Strings The Volume Conjecture and Topological Strings

2009-03-12

arxiv.org/abs/0903.2084v2

Fortsch.Phys.57:825-856,2009

Physics

High Energy Physics

High Energy Physics - Theory

52 pages, 10 figures, references added, typos corrected, comments included

Scientific paper

10.1002/prop.200900067

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.

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