A Mathematical Theory of the Topological Vertex

Abstract

We have developed a mathematical theory of the topological vertex--a theory that was original proposed by M. Aganagic, A. Klemm, M. Marino, and C. Vafa in hep-th/0305132 on effectively computing Gromov-Witten invariants of smooth toric Calabi-Yau threefolds derived from duality between open string theory of smooth Calabi-Yau threefolds and Chern-Simons theory on three manifolds.

66 pages, 10 figures; notation simplified, references added

References in corpus (4)

• The Topological Vertex
• All Loop Topological String Amplitudes From Chern-Simons Theory
• Hodge integrals and invariants of the unknot
• Localization and Gluing of Topological Amplitudes

Cited by in corpus (22)

• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Crepant resolutions and open strings
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Stable maps to Looijenga pairs
• Crystal melting on toric surfaces
• Open Gromov-Witten invariants and SYZ under local conifold transitions
• The Gerby Gopakumar-Mariño-Vafa Formula
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Toric geometry of $G_2$-manifolds
• Gromov-Witten Invariants of Local P^2 and Modular Forms
• Open/closed Correspondence via Relative/local Correspondence
• Stable maps to Looijenga pairs: orbifold examples
• On explicit formulae of LMOV invariants
• Open/Closed BPS Correspondence and Integrality
• Three-partition Hodge integrals and the topological vertex
• KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions
• Fermionic gluing principle of the topological vertex
• The log-open correspondence for two-component Looijenga pairs
• Enumerative geometry of surfaces and topological strings
• The orbifold DT/PT vertex correspondence
• Open WDVV Equations and Frobenius Structures for Toric Calabi-Yau 3-Folds