The open mirror theorem for semi-Fano toric manifolds

Let $X$ be a semi-Fano toric manifold, meaning that its anti-canonical divisor $-K_X$ is nef. Let $W^{\text{HV}}$ and $W^{\text{LF}}$ denote its Hori–Vafa and Lagrangian Floer superpotentials, respectively, and let $t(q)=\psi^{-1}(q)$ be the inverse toric mirror map. The open mirror theorem conjecture. The superpotentials satisfy

$$W^{\text{HV}}_{t(q)}=W^{\text{LF}}_q.$$

This identifies the two constructions of the mirror superpotential; the source notes that the conjecture is directly verified in the Fano case, while the semi-Fano statement concerns the instanton corrections from open Gromov–Witten invariants.