Topological String on Toric CY3s in Large Complex Structure Limit

Drissi, Lalla Btissam; Jehjouh, Houda; Saidi, El Hassan

Topological String on Toric CY3s in Large Complex Structure Limit

Authors

Drissi, Lalla Btissam

Jehjouh, Houda

Saidi, El Hassan

Description

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 $μ$ toric CY3-folds in terms of supersymmetric gauged linear sigma model with \emph{non zero} gauge invariant superpotentials $% \mathcal{W}(Φ) $. Then, we focus on a one complex parameter supersymmetric $U(1) $ gauged model involving six chiral superfields ${Φ_{i}}$ with $\mathcal{W}=μ(\prod\nolimits_{i=0}^{5}Φ_{i}) $ and we use it to compute the function $\mathcal{Z}_{top}$ for the case of the local elliptic curve in the limit $μ\to \infty $.
Latex, 38 pages, 12 figures. To appear in Nucl Phys B