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arXiv · 0903.2084

The Volume Conjecture and Topological Strings

Robbert Dijkgraaf·Hiroyuki Fuji
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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.

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Robbert Dijkgraaf, Hiroyuki Fuji. 2009-03-31. The Volume Conjecture and Topological Strings. https://doi.org/10.1002/prop.200900067

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