Large N Duality, Lagrangian Cycles, and Algebraic Knots

D. E. Diaconescu, V. Shende, C. Vafa

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)813-863
Number of pages51
JournalCommunications In Mathematical Physics
Volume319
Issue number3
DOIs
StatePublished - May 2013

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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