Communications in Mathematical Physics

, Volume 287, Issue 1, pp 117–178

Remodeling the B-Model

  • Vincent Bouchard
  • Albrecht Klemm
  • Marcos Mariño
  • Sara Pasquetti
Article

DOI: 10.1007/s00220-008-0620-4

Cite this article as:
Bouchard, V., Klemm, A., Mariño, M. et al. Commun. Math. Phys. (2009) 287: 117. doi:10.1007/s00220-008-0620-4

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 Ap 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 \({{mathbb {C}}^3 /{mathbb{Z}}_3}\) .

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Vincent Bouchard
    • 1
  • Albrecht Klemm
    • 2
  • Marcos Mariño
    • 3
  • Sara Pasquetti
    • 4
  1. 1.Jefferson Physical LaboratoryHarvard UniversityCambridgeUSA
  2. 2.Physikalisches Institut der Universität BonnBonnGermany
  3. 3.Department of PhysicsCERNGeneva 23Switzerland
  4. 4.Institut de PhysiqueUniversité de NeuchâtelNeuchâtelSwitzerland