Torus Knots and Mirror Symmetry |
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Authors: | Andrea Brini Marcos Mari?o Bertrand Eynard |
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Institution: | 1. Département de Physique Théorique et Section de Mathématiques, Université de Genève, 1211, Geneva, witzerland 2. Department of Theoretical Physics, CERN, 1213, Geneva, Switzerland 3. Service de Physique Théorique de Saclay, 91191, Gif-sur-Yvette Cedex, France
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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 ${{\rm Sl}(2, \mathbb {Z})}$ symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated with 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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