Local Mirror Symmetry for the Topological Vertex

Abstract

For three-partition triple Hodge integrals related to the topological vertex, we derive Eynard-Orantin type recursion relations from the cut-and-join equation. This establishes a version of local mirror symmetry for the local $C^3$ geometry with three D-branes, as proposed by Marino and Bouchard-Klemm-Marino-Pasquetti.

References in corpus (8)

• D-Branes And Mirror Symmetry
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• 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
• Invariants of algebraic curves and topological expansion
• Bouchard-Klemm-Marino-Pasquetti Conjecture for ${\mathbb{C}}^3$
• The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers

Cited by in corpus (13)

• 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
• 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
• Geometrical interpretation of the topological recursion, and integrable string theories
• String and dilaton equations for counting lattice points in the moduli space of curves
• Open String Invariants and Mirror Curve of the Resolved Conifold
• Reconstructing GKZ via topological recursion
• 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
• Equivariant Gromov-Witten Theory of Affine Smooth Toric Deligne-Mumford Stacks