Single-valuedness of the AdS Veneziano Amplitude

We consider the Veneziano amplitude for the scattering of gluons in type IIBstring theory on AdS_5 × S^5/ℤ_2 in the presence of D7 branes.On general grounds curvature corrections around flat space can be thought of asarising from the extra insertion of soft gravitons. This naturally leads to anopen string world-sheet representation with the extra insertion ofsingle-valued functions evaluated on the real line. We check that the recentlyobtained first curvature correction is of this form and use this new constraintto compute the second curvature correction of the AdS Veneziano amplitude.