Gromov-Witten invariants of toric Calabi-Yau threefolds
Chiu-Chu Melissa Liu
TL;DR
This paper discusses the mathematical formulation of the topological vertex, an algorithm for computing Gromov-Witten invariants of non-singular toric Calabi-Yau threefolds, based on large N duality and topological string theory.
Contribution
It provides a detailed mathematical description of the topological vertex theory developed by Li, Liu, Zhou, and the author.
Findings
Mathematical formulation of the topological vertex
Connection between topological string theory and Gromov-Witten invariants
Framework applicable to all genera of toric Calabi-Yau threefolds
Abstract
Based on the large N duality relating topological string theory on Calabi-Yau 3-folds and Chern-Simons theory on 3-manifolds, M. Aganagic, A. Klemm, M. Marino and C. Vafa proposed the topological vertex (hep-th/0305132), an algorithm on computing Gromov-Witten invariants in all genera of any non-singular toric Calabi-Yau 3-fold. In this expository article, we describe the mathematical theory of the topological vertex developed by J. Li, K. Liu, J. Zhou, and the author (math/0408426).
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Algebraic structures and combinatorial models