The excitation of a charged string passing through a shock wave in a charged Aichelburg-Sexl spacetime

We investigate how much a first-quantized charged bosonic test string gets excited after crossing a shock wave generated by a charged particle with mass M̃ and charge Q̃. On the basis of Kaluza-Klein theory, we pay attention to a closed string model where charge is given by a momentum along a compactified extra-dimension. The shock wave is given by a charged Aichelburg-Sexl (CAS) spacetime where Q̃=0 corresponds to the ordinary Aichelburg-Sexl one. We first show that the CAS spacetime is a solution to the equations of motion for the metric, the gauge field, and the axion field in the low-energy limit. Secondly, we compute the mass expectation value of the charged test string after passing through the shock wave in the CAS spacetime. In the case of small Q̃, gravitational and Coulomb forces are canceled out each other and hence the excitation of the string remains very small. This is independent of the particle mass M̃ or the strength of the shock wave. In the case of large Q̃, however, every charged string gets highly excited by quantum fluctuation in the extra-dimension caused by both the gauge and the axion fields. This is quite different from classical "molecule", which consists of two electrically charged particles connected by a classical spring.