Scattering amplitudes of regularized bosonic strings

We compute scattering amplitudes of the regularized bosonic Nambu-Goto string in the mean-field approximation, disregarding fluctuations of the Lagrange multiplier and an independent metric about their mean values. We use the previously introduced Lilliputian scaling limit to recover the Regge behavior of the amplitudes with the usual linear Regge trajectory in space-time dimensions d>2. We demonstrate a stability of this minimum of the effective action under fluctuations for d<26.