On the Hagedorn Behaviour of Singular Scale-Invariant Plane Waves

TL;DR

This paper investigates string behavior in singular scale-invariant plane wave backgrounds, revealing that their thermodynamic properties mirror those in flat space, contrasting with other plane wave models.

Contribution

It demonstrates that scale invariance leads to Hagedorn behavior identical to flat space, even with RR or NS fields, unlike other plane wave backgrounds.

Findings

Hagedorn behavior in these backgrounds matches flat space.

Scale invariance dictates thermodynamic properties.

Contrasts with BFHP plane wave behavior.

Abstract

As a step towards understanding the properties of string theory in time-dependent and singular spacetimes, we study the divergence of density operators for string ensembles in singular scale-invariant plane waves, i.e. those plane waves that arise as the Penrose limits of generic power-law spacetime singularities. We show that the scale invariance implies that the Hagedorn behaviour of bosonic and supersymmetric strings in these backgrounds, even with the inclusion of RR or NS fields, is the same as that of strings in flat space. This is in marked contrast to the behaviour of strings in the BFHP plane wave which exhibit quantitatively and qualitatively different thermodynamic properties.