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The mirror of a projective toric manifold $X_\Sigma$ is given by aLandau-Ginzburg model $(Y,W)$. We introduce a class of Lagrangian submanifoldsin $(Y,W)$ and show that, under the SYZ mirror transformation, they can betransformed to torus-invariant hermitian metrics on holomorphic line bundlesover $X_\Sigma$. Through this geometric correspondence, we also identify themirrors of Hermitian-Einstein metrics, which are given by distinguishedLagrangian sections whose potentials satisfy certain Laplace-type equations.

Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations