The volume conjecture and topological strings

Abstract

AbstractIn 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.