Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds

Abstract

We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm, Marino, and Vafa of the Gromov-Witten theory of local Calabi-Yau toric 3-folds are proven to be correct in the full 3-leg setting.

arXiv comment46 pages

References in corpus (6)

• Curve counting via stable pairs in the derived category
• Framed knots at large N
• Hodge integrals and degenerate contributions
• Quantum Calabi-Yau and Classical Crystals
• The 3-fold vertex via stable pairs
• Donaldson-Thomas theory of A_n x P^1

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• Stable maps to Looijenga pairs
• Counting invariants for the ADE McKay quivers
• Stable maps to Looijenga pairs: orbifold examples
• HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
• Entanglement entropy and edge modes in topological string theory: I
• The quantum differential equation of the Hilbert scheme of points in the plane
• Geometry and Combinatorics of Crystal Melting
• Open problems (for AGNES)
• Gromov-Witten invariants of toric Calabi-Yau threefolds
• The open string McKay correspondence for type A singularities
• Descendent theory for stable pairs on toric 3-folds