Quantum string scattering in a cosmic-string space-time.

Abstract

We exactly quantize fundamental strings propagating in a straight cosmic-string space-time (conical space-time with deficit angle $8\ensuremath{\pi}G\ensuremath{\mu}$, $\ensuremath{\mu}$ being the cosmic-string tension). If the fundamental string collides with the cosmic string the scattering is inelastic since the internal modes of the fundamental string become excited. If there is no collision, the fundamental string only suffers a deflection of $\ifmmode\pm\else\textpm\fi{}4\ensuremath{\pi}G\ensuremath{\mu}$. If there is collision we find inelastic particle production from the interaction of the string with the (classical) geometry. The string oscillator modes only suffer a change of polarization (rotation) in the elastic case and a Bogoliubov transformation in the inelastic case. As a consequence, for a given initial state, the final particle may be in any state associated with the string oscillators. All transformations are explicitly calculated in closed form. Finally, the quantum scattering amplitude for the lowest scalar (tachyon) is computed exactly. In this calculation the vertex operator in the conical geometry and the oscillator linear transformations we find here are used thoroughly. The peculiar features of the string propagation in this topologically nontrivial space-time are discussed including the question whether string splitting can occur at the classical level.