Gromov-Witten theory and Donaldson-Thomas theory, I

Abstract

We conjecture an equivalence between the Gromov-Witten theory of 3-folds and the holomorphic Chern-Simons theory of Donaldson and Thomas. For Calabi-Yau 3-folds, the equivalence is defined by the change of variables eiu = -q, where u is the genus parameter of Gromov-Witten theory and q is the Euler characteristic parameter of Donaldson-Thomas theory. The conjecture is proven for local Calabi-Yau toric surfaces. © Foundation Compositio Mathematica 2006.