Local Mirror Symmetry for One-Legged Topological Vertex

Abstract

We prove the Bouchard-Mariño Conjecture for the framed one-legged topological vertex by deriving the Eynard-Orantin type recursion relations from the cut-and-join equation satisfied by the relevant triple Hodge integrals. This establishes a version of local mirror symmetry for the local $C^3$ geometry with one $D$-brane.

First revised version

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Cited by in corpus (24)

• Intersection numbers of spectral curves
• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
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• A generalized topological recursion for arbitrary ramification
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Open topological strings and integrable hierarchies: Remodeling the A-model
• A short overview of the "Topological recursion"
• Local Mirror Symmetry for the Topological Vertex
• On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds
• All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
• Nonlinear PDEs for Fredholm determinants arising from string equations
• Invariants of spectral curves and intersection theory of moduli spaces of complex curves
• Geometrical interpretation of the topological recursion, and integrable string theories
• Quantum Mirror Curves for ${\mathbb{C}}^3$ and the Resolved Confiold
• Open String Invariants and Mirror Curve of the Resolved Conifold
• A matrix model for the topological string II: The spectral curve and mirror geometry
• Log topological recursion through the prism of $x-y$ swap
• On a proof of the Bouchard-Sulkowski conjecture
• The SYZ mirror symmetry and the BKMP remodeling conjecture
• The Laplace transform of the cut-and-join equation of Mariño-Vafa formula and its applications
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• Equivariant Gromov-Witten Theory of Affine Smooth Toric Deligne-Mumford Stacks
• On Some Mathematics Related to the Interpolating Statistics
• Topological recursion, topological quantum field theory and Gromov-Witten invariants of BG