Classical dynamics of strings with rigidity

We explore the classical dynamics of strings with rigidity, i.e., with terms added to the string action which depend on the extrinsic curvature of the world sheet. We study classical solutions of the string equations of motion using both analytical and numerical methods, and we determine the leading Regge trajectories J($E^2$) for a set of classical rotating string configurations. We observe that for open strings the dominant classical solutions are identical to those for the conventional Nambu string, and correspondingly give linear trajectories. However, for closed strings we find new solutions that include finite-energy, static configurations, and that give trajectories which are nonlinear as the lowest-energy solution is approached, but become linear asymptotically as J($E^2$)→∞.