Remodeling the B-model

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 Wilson loops in lens spaces. We also use our formalism to predict the disk amplitude for the orbifold C^3/Z_3.

83 pages, 9 figures

References in corpus (20)

• Phases of $N=2$ Theories In Two Dimensions
• 2D Gravity and Random Matrices
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Geometric Engineering of Quantum Field Theories
• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Knot Invariants and Topological Strings
• All genus correlation functions for the hermitian 1-matrix model
• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• Matrix Model as a Mirror of Chern-Simons Theory
• Matrix Model Calculations beyond the Spherical Limit
• Hermitean matrix model free energy: Feynman graph technique for all genera
• Chern-Simons Theory and Topological Strings
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Direct Integration of the Topological String
• Topological String Partition Functions as Polynomials
• Breakdown of universality in multi-cut matrix models
• Holomorphic anomaly and matrix models
• A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariant of 3d Manifolds I
• Double Scaling Limits and Twisted Non-Critical Superstrings

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