Remodeling the B-model

TL;DR

This paper introduces a comprehensive formalism for calculating B-model amplitudes in local Calabi-Yau geometries, unifying open and closed string computations and enabling analysis of stringy phase transitions.

Contribution

It develops a new recursive formalism based on matrix models for unambiguous, non-perturbative B-model amplitudes applicable across different moduli space phases.

Findings

Validated the formalism with checks at orbifold points

Computed the 't Hooft expansion of Wilson loops in lens spaces

Predicted the disk amplitude for orbifold C^3/Z_3

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.