Quantum string scattering in the Aichelburg-Sexl geometry

Abstract

At energies of the order or larger than the Planck mass, the curved space-time geometry created by the particles dominates their collision process. The so-called Aichelburg-Sexl (AS) metric is relevant in this problem. We find the exact solution to the quantization and scattering of a closed bosonic string in D-dimensional AS geometry. The mass spectrm and critical dimension are the same as in flat space-time but there is non-trivial elastic and inelastic scattering by the shock wave. We find the exact (non-linear) and the Bogoliubov (linear) transformations relating the ingoing and outgoing string mode operators. The transition amplitudes between the internal modes and the total pair-creation rate are computed (this pair mode creation is a genuine string effect which does not exist in the quantum point particle theory). We find the deflection angle and the quantum string corrections to the classical cross section. The ground-state scattering amplitude is analyzed. Comparison with the black-hole results and recent investigations of string collisions in flat space-time are discussed.