Off-shell tachyon amplitudes: analyticity and projective invariance
  We compute off-shell three- and four-tachyon amplitudes at tree level by using a prescription based on the requirement of projective invariance. In particular we show that the off-shell four-tachyon amplitude can be put in the same form as the corresponding on-shell one, exhibiting therefore the same analyticity properties. This is shown both for the bosonic and the fermionic string. The result obtained in the latter case can be extended to the off-shell four-tachyon amplitude in type 0 theory. 
F. Cuomo, R. Marotta, F. Nicodemi, R. Pettorino, F. Pezzella and G.   Sabella