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The Volume Conjecture and Topological Strings

Dijkgraaf, R.H. and Fuji, H. (2009) The Volume Conjecture and Topological Strings. Fortschritte der Physik, 59(9), 825-856. ISSN 00158208. doi: 10.1002/prop.200900067.


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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.

Item Type:Article
Additional Information:doi: 10.1002/prop.200900067
Institutes:Bureau KNAW
ID Code:3871
Deposited On:27 Aug 2009 11:36
Last Modified:13 Oct 2010 22:35

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