Boundary terms in Nambu-Goto string action

We investigate classical strings defined by the Nambu-Goto action with the boundary term added. We demonstrate that the latter term has a significant bearing on the string dynamics. It is confirmed that new action terms that depend on higher order derivatives of string coordinates cannot be considered as continuous perturbations from the starting string functional. In the case the boundary term reduces to the Gauss-Bonnet term, a stability analysis is performed on the rotating rigid string solution. We determined the most generic solution that the fluctuations grow to. Longitudinal string excitations are found. The Regge trajectories are nonlinear.Comment: 9 LaTeX pages and 3 PostScript figures (uuencoded), preprint TPJU-15/9

Classical Open String Models in 4-Dim Minkowski Spacetime

Classical bosonic open string models in fourdimensional Minkowski spacetime are discussed. A special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider lagrangians that can depend on second order derivatives of worldsheet coordinates. A revised interpretation of the variational problem for such theories is given. We derive a general form of a boundary term that can be added to the open string action to control edge conditions and modify conservation laws. An extended boundary problem for minimal surfaces is examined. Following the treatment of this model in the geometric approach, we obtain that classical open string states correspond to solutions of a complex Liouville equation. In contrast to the Nambu-Goto case, the Liouville potential is finite and constant at worldsheet boundaries. The phase part of the potential defines topological sectors of solutions.Comment: 25 pages, LaTeX, preprint TPJU-28-93 (the previous version was truncated by ftp...