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.