Flat-space limit of defect correlators and stringy AdS form factors

We study AdS form factors, given by the Mellin representation for CFT correlators of local operators in the presence of extended defects. We propose a formula for taking (and expanding around) the flat-space limit. This formula relates the flat-space form factors for particles scattering off an extended object to the high-energy limit of the Mellin amplitude, via a Borel transform. We check the validity of our proposal in a number of examples. As an application, we study the two-point function of local operators in the presence of a 't Hooft loop in 4d $\mathcal{N}=4$ SYM, and compute the first few orders of stringy corrections to the AdS form factor of gravitons scattering off a D1 brane.