Torus knots and mirror symmetry
High Energy Physics - Theory
2015-05-28 v1 Mathematical Physics
Algebraic Geometry
Geometric Topology
math.MP
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.
Keywords
Cite
@article{arxiv.1105.2012,
title = {Torus knots and mirror symmetry},
author = {Andrea Brini and Bertrand Eynard and Marcos Marino},
journal= {arXiv preprint arXiv:1105.2012},
year = {2015}
}
Comments
30 pages + appendix, 3 figures