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Large N Duality, Lagrangian Cycles, and Algebraic Knots

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Abstract

We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.

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Authors and Affiliations

  1. NHETC, Rutgers University, Piscataway, NJ, 08854-0849, USA

    D.-E. Diaconescu

  2. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    V. Shende

  3. Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, USA

    C. Vafa

Authors
  1. D.-E. Diaconescu
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  2. V. Shende
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  3. C. Vafa
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Correspondence to D.-E. Diaconescu.

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Communicated by N. A. Nekrasov

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Diaconescu, DE., Shende, V. & Vafa, C. Large N Duality, Lagrangian Cycles, and Algebraic Knots. Commun. Math. Phys. 319, 813–863 (2013). https://doi.org/10.1007/s00220-012-1563-3

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  • DOI: https://doi.org/10.1007/s00220-012-1563-3

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