Higher-genus Calabi–Yau/Saito–Givental mirror symmetry

Let $W$ be a Calabi–Yau polynomial, let $G_W$ be the group appearing in the quotient $[X_W/\widetilde{G}_W]$, and let $W^{\vee}_{\infty}=\prod_i x_i$ be the large complex structure point of the mirror deformation. Let $\mathcal F^g_{\operatorname{GW}}$ denote the genus-$g$ Gromov–Witten potential and $\mathcal F^g_{\operatorname{formal}}$ the genus-$g$ formal Saito–Givental potential. CY/LG higher-genus mirror symmetry. There is a mirror map matching a neighborhood of

$$H^{1,1}_{\operatorname{CR}}([X_W/\widetilde{G}_W];\mathbb C)$$

with a neighborhood of $W^{\vee}_{\infty}$ such that $\mathcal F^g_{\operatorname{GW}}$ is matched to $\mathcal F^g_{\operatorname{formal}}$. This is one of the higher-genus mirror conjectures governing the LG–CY correspondence; the source does not report a general proof.