Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 306 / 1 / d / Solution

A rigidly rotating stretched solution iswith all other coordinates constant. Each coordinate obeys the wave equation and $X^{\prime }=0$ at $\sigma =0,\pi$. Directly, $\dot{X}\cdot X^{\prime }=0$ andso both Virasoro constraints hold. Its energy and planar angular momentum areConsequently $J=M^2/(2\pi T)={\alpha }^{\prime }{M}^2$, the classical leading open-string Regge trajectory.