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.

26 pages

References in corpus (10)

• The open Gromov-Witten-Welschinger theory of blowups of the projective plane
• Stable maps to Looijenga pairs
• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Open/closed Correspondence via Relative/local Correspondence
• Open/Closed BPS Correspondence and Integrality
• Examples of relative quantum cohomology
• Orbifold Open/Closed Correspondence and Mirror Symmetry
• Integrable systems of finite type from F-cohomological field theories without unit
• WDVV-based recursion for open Gromov-Witten invariants
• Open Gromov-Witten invariants from the Fukaya category