Annales Henri Poincaré

, Volume 13, Issue 8, pp 1873–1910 | Cite as

Torus Knots and Mirror Symmetry



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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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Andrea Brini
    • 1
  • Marcos Mariño
    • 1
  • Bertrand Eynard
    • 2
    • 3
  1. 1.Département de Physique Théorique et Section de MathématiquesUniversité de GenèveGenevawitzerland
  2. 2.Department of Theoretical PhysicsCERNGenevaSwitzerland
  3. 3.Service de Physique Théorique de SaclayGif-sur-Yvette CedexFrance

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