Torus knots and mirror symmetry

Andrea Brini, Marcos Mariño*, Bertrand Eynard

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


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 S1(2ℤ) 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.

Original languageEnglish
Pages (from-to)1873-1910
Number of pages38
JournalAnnales Henri Poincare
Issue number8
Early online date29 Mar 2012
Publication statusPublished - 1 Dec 2012


  • Matrix Model
  • Open String
  • Wilson Line
  • Topological String
  • Spectral Curve

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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