Gromov-Witten invariants 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).

18 pages, 9 figures; dedicated to Shing-Tung Yau on the occasion of his 59th birthday

References in corpus (9)

• Curve counting via stable pairs in the derived category
• An algebro-geometric proof of Witten's conjecture
• The 3-fold vertex via stable pairs
• A simple proof of Witten conjecture through localization
• A Conjecture on Hodge Integrals
• Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
• Integration Theory for Zero Sets of Polyfold Fredholm Sections
• Localization, Hurwitz Numbers and the Witten Conjecture