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 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 × 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 non-zero gauge invariant superpotentials W ( Φ ) . Then, we focus on a one complex parameter supersymmetric U ( 1 ) gauged model involving six chiral superfields { Φ i } with W = μ ( ∏ i = 0 5 Φ i ) and we use it to compute the function Z top for the case of the local elliptic curve in the limit μ → ∞ .