The Donaldson–Thomas/Gromov–Witten correspondence for Calabi–Yau threefolds

Let $X$ be a Calabi–Yau threefold, meaning that $K_X$ is trivial. For curve classes $\beta\ne0$, let $Z^{\mathrm{DT}}(X)'$ be the reduced Donaldson–Thomas partition function, and let

$$Z^{\mathrm{GW}}(X)'=\exp\left(\sum_g\lambda^{2g-2}\sum_{\beta\ne0}N^g_\beta t^\beta\right)$$

be the reduced Gromov–Witten partition function, where $N^g_\beta$ denotes the genus-$g$ Gromov–Witten invariant. The Donaldson–Thomas/Gromov–Witten correspondence. The reduced partition functions satisfy

$$Z^{\mathrm{DT}}(X)'=Z^{\mathrm{GW}}(X)'$$

after the change of variables $q=-e^{i\lambda}$. This correspondence predicts equality between two curve-counting theories after a nontrivial change of variables and is a central relation between Donaldson–Thomas and Gromov–Witten invariants. The supplied text does not establish its general status.