  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.
