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Remodeling the B-Model

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Abstract

We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi–Yau geometries, including the mirrors of toric manifolds. The formalism is based on the recursive solution of matrix models recently proposed by Eynard and Orantin. The resulting amplitudes are non-perturbative in both the closed and the open moduli. The formalism can then be used to study stringy phase transitions in the open/closed moduli space. At large radius, this formalism may be seen as a mirror formalism to the topological vertex, but it is also valid in other phases in the moduli space. We develop the formalism in general and provide an extensive number of checks, including a test at the orbifold point of A p fibrations, where the amplitudes compute the ’t Hooft expansion of vevs of Wilson loops in Chern-Simons theory on lens spaces. We also use our formalism to predict the disk amplitude for the orbifold \({{mathbb {C}}^3 /{mathbb{Z}}_3}\) .

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Authors and Affiliations

  1. Jefferson Physical Laboratory, Harvard University, 17 Oxford St., Cambridge, MA, 02138, USA

    Vincent Bouchard

  2. Physikalisches Institut der Universität Bonn, Nußallee 12, D-53115, Bonn, Germany

    Albrecht Klemm

  3. Department of Physics, CERN, 1211, Geneva 23, Switzerland

    Marcos Mariño

  4. Institut de Physique, Université de Neuchâtel, Rue A. L. Breguet 1, CH-2000, Neuchâtel, Switzerland

    Sara Pasquetti

Authors
  1. Vincent Bouchard
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  2. Albrecht Klemm
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  3. Marcos Mariño
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  4. Sara Pasquetti
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Corresponding author

Correspondence to Marcos Mariño.

Additional information

Communicated by M.R. Douglas

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Bouchard, V., Klemm, A., Mariño, M. et al. Remodeling the B-Model. Commun. Math. Phys. 287, 117–178 (2009). https://doi.org/10.1007/s00220-008-0620-4

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  • DOI: https://doi.org/10.1007/s00220-008-0620-4

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