Open WDVV equations and Frobenius structures for toric Calabi-Yau 3-folds

Abstract

Let X be a toric Calabi-Yau 3-fold and let $L\subset X$ be an Aganagic-Vafa outer brane. We prove two versions of open WDVV equations for the open Gromov-Witten theory of $(X,L)$ . The first version of the open WDVV equation leads to the construction of a semi-simple (formal) Frobenius manifold, and the second version leads to the construction of a flat (formal) F-manifold.

Keywords

• 14N35
• 53D45