Topological String on Toric CY3s in Large Complex Structure Limit

Abstract

We develop a non planar topological vertex formalism and we use it to study the A-model partition function ${\mathcal{Z}}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that purpose, we first consider the $T^2\times R$ special Lagrangian fibration of generic CY3-folds and we give the realization of the class of large $\mu$ toric CY3-folds in terms of supersymmetric gauged linear sigma model with \emph{non zero} gauge invariant superpotentials . Then, we focus on a one complex parameter supersymmetric $U(1)$ gauged model involving six chiral superfields ${\Phi }_i$ with $\mathcal{W}=\mu ({\prod }_{i=0}^5{\Phi }_i)$ and we use it to compute the function ${\mathcal{Z}}_{top}$ for the case of the local elliptic curve in the limit $\mu \to \infty$.

Latex, 38 pages, 12 figures. To appear in Nucl Phys B

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Cited by in corpus (2)

• Refining the Shifted Topological Vertex
• Quiver Gauge Models in F-Theory on Local Tetrahedron