- The volume conjecture and topological strings
- Fortschritte der Physik
- Volume | Issue number
- 57 | 9
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Institute for Theoretical Physics Amsterdam (ITFA)
Korteweg-de Vries Institute for Mathematics (KdVI)
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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