  We discuss the flat space limit of AdS using the momentum space
representation of CFT correlators. The flat space limit involves sending the
AdS radius and the dimensions of operators dual to massive fields to infinity
while also scaling appropriately the sources of the dual operators. In this
limit, d-dimensional CFT correlators become (d+1)-dimensional scattering
amplitudes. We exemplify our discussion with the computation of the flat-space
limit of the CFT 3-point function of a conserved current, a non-conserved
charged vector operator and its conjugate. The flat-space limit should yield
the scattering amplitude of an Abelian gauge field with two massive vector
fields. This scattering amplitude computes the electromagnetic form factors of
the electromagnetic current in a spin-1 state, and these form factors encode
the electromagnetic properties of the massive vector field (charge, magnetic
moment and quadruple moment). In terms of the CFT, the flat-space limit amounts
to zooming in the infrared region of the triple-K integrals that determine the
3-point function, while also scaling to infinity the order of (some of) the
Bessel functions that feature in the triple-K integrals. In this limit the
triple-K integral becomes proportional to the energy-preserving delta function,
and the flat space limit correctly yields the corresponding flat space
scattering amplitude in complete detail.
