Relative descendent Gromov–Witten/Pandharipande–Thomas correspondence

Let $M$ be a smooth projective threefold, let $D$ be a connected divisor, let $\alpha=(\alpha_1,\ldots,\alpha_r)$ be a partition, let $\gamma_j\in H^*(M,\mathbb{Q})$ be even classes, and let $\eta$ be relative boundary data. Under the variable change $e^{iu}=-q$,

Relative descendent GW/PT correspondence.

$$(-q)^{-\mathsf{c}_\beta^M/2}\operatorname{Z_{PT}}\left(M/D;q\mid\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_r-1}(\gamma_r)\mid\eta\right)_\beta = (-iu)^{\mathsf{c}_\beta^M+\ell(\eta)-|\eta|}\operatorname{Z_{GW}^{\prime}}\left(M/D;u\mid\overline{\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_r-1}(\gamma_r)}\mid\eta\right)_\beta.$$

This is the relative descendent refinement of the GW/PT correspondence, with the logarithmic tangent bundle governing the relative descendent transformation.