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

We study AdS form factors, given by the Mellin representation for CFT correlatorsof local operators in the presence of extended defects. We propose a formula for taking (andexpanding around) the flat-space limit. This formula relates the flat-space form factors forparticles 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. Asan application, we study the two-point function of local operators in the presence of a 'tHooft loop in 4dN= 4SYM, and compute the first few orders of stringy corrections tothe AdS form factor of gravitons scattering off a D1 brane.