A note on on-shell recursion relation of string amplitudes
  In the application of on-shell recursion relation to string amplitudes, one challenge is the sum over infinite intermediate on-shell string states. In this note, we show how to sum these infinite states explicitly by including unphysical states to make complete Fock space. 
Yung-Yeh Chang, Bo Feng, Chih-Hao Fu, Jen-Chi Lee, Yihong Wang and Yi   Yang
hep-th hep-ph