Can free strings propagate across plane wave singularities?

TL;DR

This paper investigates whether free strings can pass through plane wave singularities, finding that finite excitation energy constraints generally prevent propagation unless additional scales are introduced.

Contribution

It establishes a connection between string mode evolution and center-of-mass motion near singularities, highlighting the necessity of scale introduction for consistent propagation.

Findings

Propagation is generally inconsistent without additional scales.

Finite excitation energy constraints exclude crossing the singularity.

Scale-invariance is broken unless scales are introduced at the singularity.

Abstract

We study free string propagation in families of plane wave geometries developing strong scale-invariant singularities in certain limits. We relate the singular limit of the evolution for all excited string modes to that of the center-of-mass motion (the latter existing for discrete values of the overall plane wave profile normalization). Requiring that the entire excitation energy of the string should be finite turns out to be quite restrictive and essentially excludes consistent propagation across the singularity, unless dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).