Large N duality, lagrangian cycles, and algebraic knots

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 explicity 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.

53 pages, latex

References in corpus (4)

• The Refined Topological Vertex
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Wall Crossing and M-theory
• Chern-Simons Invariants of Torus Links

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• The Condensate from Torus Knots
• BPS states, torus links and wild character varieties
• Worldsheet Interpretation of the Level-Rank Duality
• Stable maps to Looijenga pairs: orbifold examples
• A support theorem for Hilbert schemes of planar curves, II
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• A String Dual for Partially Topological Chern-Simons-Matter Theories
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