Rotations of a closed string with the Nambu Lagrangian

In addition to widely known rotations of a linear string, rotations of a closed string, whose shape is more complex, also exist. For a closed string with the simplest Nambu geometric Lagrangian, solutions containing a singularity are investigated and the corresponding linear Regge trajectories are determined. Two domains of solutions exist: (1) solutions with the slope of trajectories larger than α'/4 and circular velocities smaller than the velocity of light and (2) solutions with the slope of trajectories smaller than α'/4 and circular velocities exceeding the velocity of light. A generalization of rotations of a string is considered, for which the right x = fR(τ - σ) and the left s + fL(τ + σ) rotations are executed about axes differently oriented in space. These more complex solutions are not pure rotations, but describe a continuous transition from the first to the second domain of rotational solutions. These solutions can be quantized. The found states should be considered as a string model of quark-free hadrons, i.e., glueballs