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

TL;DR

This paper studies how a charged string gets excited after crossing a shock wave in a charged Aichelburg-Sexl spacetime, revealing that large charge induces significant quantum excitations, unlike the small charge case where effects cancel out.

Contribution

It introduces a model for charged strings in a charged shock wave background and analyzes their excitation, highlighting the effects of charge magnitude on quantum string behavior.

Findings

Small charge leads to negligible string excitation due to force cancellation.

Large charge causes significant quantum excitation of the string.

The behavior differs from classical charged particle systems, emphasizing quantum effects.

Abstract

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 $\tilde{M}$ and charge $\tilde{Q}$. 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 $\tilde{Q}=0$ 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 $\tilde{Q}$, 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 $\tilde{M}$ or the strength of the shock wave. In the case of large $\tilde{Q}$, 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.