On the Singularity Structure and Stability of Plane Waves

TL;DR

This paper investigates the singularity conditions and stability of plane wave backgrounds, providing a criterion for singularities and analyzing scalar mode fluctuations to assess stability despite negative mass terms.

Contribution

It introduces a simple criterion linking Brinkmann metric entries to curvature for singularity detection and discusses the potential stability of plane waves with negative mass terms.

Findings

Established a relation between metric entries and curvature for singularity criteria

Analyzed scalar mode fluctuations to assess background stability

Argued that some backgrounds with negative mass terms may still be stable

Abstract

We describe various aspects of plane wave backgrounds. In particular, we make explicit a simple criterion for singularity by establishing a relation between Brinkmann metric entries and diffeomorphism-invariant curvature information. We also address the stability of plane wave backgrounds by analyzing the fluctuations of generic scalar modes. We focus our attention on cases where after fixing the light-cone gauge the resulting world sheet fields appear to have negative "mass terms". We nevertheless argue that these backgrounds may be stable.