Torus knots and mirror symmetry

Abstract

We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.

30 pages + appendix, 3 figures

References in corpus (8)

• The Refined Topological Vertex
• Open string amplitudes and large order behavior in topological string theory
• Remodeling the B-model
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants
• Topological expansion of the Bethe ansatz, and quantum algebraic geometry
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry

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