DDF amplitudes are lightcone amplitudes and the naturalness of Mandelstam maps

Abstract We show that on-shell DDF amplitudes are on-shell lightcone amplitudes and that Mandelstam maps emerge naturally with a precise normalization, and are intrinsic to the DDF states. Off-shell DDF and Mandelstam amplitudes à la Kaku–Kikkawa differ. In the process, we give a very explicit formula for the conformal transformation of a generic vertex in the form of a compact generating function for free theories.