MNOP Gromov–Witten/Donaldson–Thomas correspondence

Let $X$ be a Calabi–Yau $3$-fold. Define the Gromov–Witten generating series by

$$\mathrm{GW}(X)=\sum_{g\geq 0,\,\beta>0}N^{\rm GW}_{g,\beta}\lambda^{2g-2}t^\beta,$$

and the reduced Donaldson–Thomas series by $\mathop{\rm DT}\nolimits'(X)=\mathop{\rm DT}\nolimits(X)/\mathop{\rm DT}\nolimits_0(X)$. MNOP Gromov–Witten/Donaldson–Thomas correspondence. After the variable change $q=-e^{i\lambda}$,

$$\exp(\mathrm{GW}(X))=\mathop{\rm DT}\nolimits'(X).$$

The correspondence relates the generally rational Gromov–Witten theory to the integer-valued Donaldson–Thomas theory and is expected to imply hidden integrality of Gromov–Witten invariants.