Orthogonal quasimodularity conjecture for Gromov–Witten potentials of Enriques surfaces

Let $M=U\oplus U(2)\oplus E_8(-2)$ be the Enriques lattice, let $\mathcal D$ be the relevant orthogonal domain, and let $\mathcal H_{-2}\subset\mathcal D$ be the norm $-2$ Noether–Lefschetz divisor. For Gromov–Witten potentials $F_g(\tau_{k_1}(\gamma_1),\ldots,\tau_{k_n}(\gamma_n))$, Enriques orthogonal quasimodularity conjecture. These potentials are components of a vector-valued logarithmic quasimodular form for the orthogonal group $O^+(M)$ with respect to the pair $(\mathcal D,\mathcal H_{-2})$. This is the paper’s main conjecture in the Enriques-surface case and is intended to connect their Gromov–Witten theory with orthogonal quasimodular forms; the source does not state a resolution.