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All Loop Topological String Amplitudes from Chern-Simons Theory

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Abstract

We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In particular we explicitly compute the topological string amplitudes for 2 up to degree 12 and 1× 1 up to total degree 10 to all genera. This also leads to certain novel large N dualities in the context of ordinary superstrings, involving duals of type II superstrings on local Calabi-Yau three-folds without any fluxes.

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Authors and Affiliations

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

    Mina Aganagic, Marcos Mariño & Cumrun Vafa

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  1. Mina Aganagic
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  2. Marcos Mariño
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  3. Cumrun Vafa
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N.A. Nekrasov

This research is supported in part by NSF grants PHY-9802709 and DMS-0074329

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Aganagic, M., Mariño, M. & Vafa, C. All Loop Topological String Amplitudes from Chern-Simons Theory. Commun. Math. Phys. 247, 467–512 (2004). https://doi.org/10.1007/s00220-004-1067-x

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