Two-point tree-level string amplitudes as AdS transition amplitudes

We compute the two-point open string and closed string amplitudes at tree level and show that, in a 't Hooft-like limit, they take a form structurally analogous to boundary-to-boundary transition amplitudes of a scalar field in Euclidean AdS space. Interestingly, while both amplitudes yield equivalent expressions, the associated 't Hooft couplings are defined by different worldsheet curvatures-geodesic for the disk and Gaussian for the sphere-suggesting a possible geometric aspect of open/closed string duality.