Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-10-21
Nucl.Phys.B849:166-211,2011
Physics
High Energy Physics
High Energy Physics - Theory
48 pages, 7 figures
Scientific paper
10.1016/j.nuclphysb.2011.03.014
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We check the correspondence for the figure eight knot complement and the once punctured torus bundle over S^1 with the holonomy L^2R up to the fourth order. For the torus knots, we find trivial the recursion relations on both sides.
Dijkgraaf Robbert
Fuji Hiroyuki
Manabe Masahide
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