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

References in corpus (21)

• Phases of $N=2$ Theories In Two Dimensions
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• The Topological Vertex
• The Refined Topological Vertex
• Quantum Calabi-Yau and Classical Crystals
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Link Homologies and the Refined Topological Vertex
• Lectures on Calabi-Yau and special Lagrangian geometry
• RG Cascades in Hyperbolic Quiver Gauge Theories
• Crystal Model for the Closed Topological Vertex Geometry
• Explicit Analysis of Kahler Deformations in 4D N=1 Supersymmetric Quiver Theories
• Topological Amplitudes and Physical Couplings in String Theory
• D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory
• Topological string in harmonic space and correlation functions in $S^3$ stringy cosmology
• D-Branes in Topological String Theory
• Super Calabi-Yau's and Special Lagrangians
• On Local Calabi-Yau Supermanifolds and Their Mirrors
• Refining the Shifted Topological Vertex
• Topological SL(2) Gauge Theory on Conifold

Cited by in corpus (5)

• Higher spin AdS${}_3$ gravity and Tits-Satake diagrams
• Finiteness of 3D higher spin gravity Landscape
• Refining the Shifted Topological Vertex
• Black hole solutions of three dimensional E${}_6$-gravity
• Quiver Gauge Models in F-Theory on Local Tetrahedron