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

TL;DR

This paper establishes a correspondence between Gromov-Witten and Donaldson-Thomas theories for nonsingular toric 3-folds, confirming the accuracy of topological vertex calculations in the full 3-leg case.

Contribution

It proves the equivariant Gromov-Witten and Donaldson-Thomas theories are equivalent for nonsingular toric 3-folds, extending the validity of topological vertex methods.

Findings

Equivalence of Gromov-Witten and Donaldson-Thomas theories for toric 3-folds

Validation of topological vertex calculations in the full 3-leg setting

Confirmation of conjectured correspondences in enumerative geometry

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.