Local Mirror Symmetry for the Topological Vertex

TL;DR

This paper establishes a local mirror symmetry framework for the topological vertex by deriving Eynard-Orantin recursion relations from cut-and-join equations, connecting topological string theory and algebraic geometry.

Contribution

It introduces a novel derivation of recursion relations for triple Hodge integrals, confirming a local mirror symmetry conjecture for the local C^3 geometry with D-branes.

Findings

Derived Eynard-Orantin recursion relations from cut-and-join equations.

Confirmed local mirror symmetry for the local C^3 geometry with D-branes.

Connected topological vertex computations with algebraic recursion techniques.

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.