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

References in corpus (6)

• Open string amplitudes and large order behavior in topological string theory
• Hodge integrals, Hurwitz numbers, and Symmetric Groups
• Invariants of algebraic curves and topological expansion
• A Conjecture on Hodge Integrals
• Bouchard-Klemm-Marino-Pasquetti Conjecture for ${\mathbb{C}}^3$
• Symmetrized cut-join equation of Marino-Vafa formula