Open String Invariants and Mirror Curve of the Resolved Conifold

Abstract

For the resolved conifold with one outer D-brane in arbitrary framing, we present some results for the open string partition functions obtained by some operator manipulations. We prove some conjectures by Aganagic-Vafa and Aganagic-Klemm-Vafa that relates such invariants to the mirror curve of the resolved conifold. This establishes local mirror symmetry for the resolved confolds for holomorphic disc invariants. We also verify an integrality conjecture of such invariants by Ooguri-Vafa in this case and present closed formulas for some Ooguri-Vafa type invariants in genus 0 and arbitrary genera.

References in corpus (9)

• Open string amplitudes and large order behavior in topological string theory
• A matrix model for simple Hurwitz numbers, and topological recursion
• Local Mirror Symmetry for One-Legged Topological Vertex
• Curve counting and instanton counting
• Invariants of algebraic curves and topological expansion
• A Conjecture on Hodge Integrals
• Bouchard-Klemm-Marino-Pasquetti Conjecture for ${\mathbb{C}}^3$
• Local Mirror Symmetry for the Topological Vertex
• Geometrical interpretation of the topological recursion, and integrable string theories

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• On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds
• All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
• Quantum Mirror Curves for ${\mathbb{C}}^3$ and the Resolved Confiold
• The SYZ mirror symmetry and the BKMP remodeling conjecture
• A Proof of the Full Marino-Vafa Conjecture