String Propagation in Gravitational Wave Backgrounds

TL;DR

This paper analyzes string behavior in gravitational wave backgrounds using a conformal field theory approach, revealing that string dynamics are confined to either transverse or longitudinal spaces, but not both simultaneously.

Contribution

It constructs all unitary irreducible representations of a current algebra using free fields and orbifolds, providing new insights into string spectra and scattering in gravitational wave backgrounds.

Findings

String dynamics occur only in transverse or longitudinal space, not both.

All irreducible representations are explicitly constructed from free fields.

The spectrum and scattering are analyzed within this framework.

Abstract

The Conformal Field Theory of the current algebra of the centrally extended 2-d Euclidean group is analyzed. Its representations can be written in terms of four free fields (without background charge) with signature ($-$+++). We construct all irreducible representations of the current algebra with unitary base out of the free fields and their orbifolds. This is used to investigate the spectrum and scattering of strings moving in the background of a gravitational wave. We find that all the dynamics happens in the transverse space or the longitunal one but not both.