The high energy behavior of open string scattering

The high energy scattering of open strings is studied using semiclassical techniques. It is shown that the integrals for the open string amplitudes are dominated by saddlepoints. In the case of orientable strings the dominant saddlepoints, to arbitrary order in perturbation theory, can be constructed from the closed string saddlepoints obtained previously. A variant of this technique is used to construct the dominant saddles for nonorientable surfaces. It is found that certain topologies do not contain dominant saddles. The one loop open string amplitudes are studied in detail to illustrate these issues. The semiclassical trajectories corresponding to these saddlepoints are described. This analysis is then applied, following the analogous treatment of the closed string, to derive an infinite set of linear relations between open string scattering amplitudes at infinite energy that hold order by order in perturbation theory. (orig.)