Large N Duality, Lagrangian Cycles, and Algebraic Knots
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Author(s)
Diaconescu, D.-E.
Vafa, C.
Shende, Vivek
Date Issued
October 2012
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
Diaconescu, D.-E., V. Shende, and C. Vafa. “Large N Duality, Lagrangian Cycles, and Algebraic Knots.” Communications in Mathematical Physics 319.3 (2013): 813–863.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00220-012-1563-3
