Torus knots and mirror symmetry

Details Torus knots and mirror symmetry Torus knots and mirror symmetry

2011-05-10

arxiv.org/abs/1105.2012v1

Physics

High Energy Physics

High Energy Physics - Theory

30 pages + appendix, 3 figures

Scientific paper

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.

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