Classical string profile for a class of DDF amplitudes

In the critical bosonic string theory, we explicitly evaluate the three point scattering amplitude at tree level, of a photon with two massive higher spins. The massive excitations belong to states of the form $A_{-r_1}^{s_1}{A}_{-r_2}^{s_2}$ where $A_{-n}$ is a DDF creation operator. Next, we take the infinite spin'' limit to arrive at the classical string dynamics. We find a rotating floppy’’ string lying mostly on a plane which develops a transverse kink.