The marked relative GW/PT correspondence

Let $(X,D)$ be the relative geometry, let $\beta$ be a curve class, let $\lambda$ be a relative boundary condition, and let $\gamma\in H^{\ast}((X,D)^r)$. The marked descendents $\tau_{\alpha_1-1}\cdots\tau_{\alpha_r-1}(\gamma)$ are transformed by the relative descendent correspondence.

The marked relative GW/PT correspondence. For all $\gamma\in H^{\ast}((X,D)^r)$, $Z^{(X,D)}_{\mathsf{PT},\beta}(\lambda\mid\tau_{\alpha_1-1}\cdots\tau_{\alpha_r-1}(\gamma))$ is the Fourier expansion of a rational function in $p$, and under $p=e^z$,

$$Z^{(X,D)}_{\mathsf{PT},\beta}(\lambda\mid\tau_{\alpha_1-1}\cdots\tau_{\alpha_r-1}(\gamma))=Z^{(X,D)}_{\mathsf{GW},\beta}(\lambda\mid\overline{\tau_{\alpha_1-1}\cdots\tau_{\alpha_r-1}(\gamma)}).$$

This extends the relative correspondence from products of pullbacks of individual insertions to arbitrary cohomology classes on $(X,D)^r$.