GW/PT correspondence for Calabi–Yau threefolds

Let $M$ be a Calabi–Yau threefold, and let $\beta$ be a nonzero curve class in $M$. The symbols $\operatorname{Z_{GW}^{\prime}}(M;u)_\beta$ and $\operatorname{Z_{PT}}(M;q)_\beta$ denote the reduced Gromov–Witten and Pandharipande–Thomas partition functions in class $\beta$. GW/PT correspondence. Under the variable change $-q=e^{iu}$, one has

$$\operatorname{Z_{GW}^{\prime}}(M;u)_\beta=\operatorname{Z_{PT}}(M;q)_\beta.$$

This is the descendent-free GW/PT correspondence for Calabi–Yau threefolds; the DT/PT correspondence is known, while the GW/PT correspondence is the conjectural equivalence of the remaining curve-counting theories.