The SYZ map as the inverse toric mirror map

Let $X$ be a semi-Fano toric manifold with complexified Kähler parameters $q=(q_1,\ldots,q_r)$, and let $\psi:\check{\mathcal{M}}_B\to\mathcal{M}_A$ be the toric mirror map. For basic disk classes $\beta_i$ and effective curve classes $\alpha$ with $c_1(\alpha)=0$, define generating functions $1+\delta_i(q)$ from the genus-zero open Gromov–Witten invariants $n_{\beta_i+\alpha}$, and define the SYZ map by

$$t^a(q)=q_a\prod_{i=1}^m(1+\delta_i(q))^{D_i\cdot\gamma_a},\qquad a=1,\ldots,r.$$

The SYZ-map conjecture. The SYZ map $\phi$ is inverse to the mirror map $\psi$. This is an equivalent formulation of the equality between the Hori–Vafa and Lagrangian Floer superpotentials; it expresses the mirror coordinates directly through open Gromov–Witten disk counts.