Plane waves from double extended spacetimes

TL;DR

This paper explores exact string backgrounds derived from double extended nonsemisimple algebras, showing they can be simplified to product spaces and analyzing their Penrose limits, including D-brane solutions.

Contribution

It demonstrates a coordinate transformation to simplify double extended algebra backgrounds and connects these to Nappi--Witten plane waves via contraction, with D-branes surviving the Penrose limit.

Findings

Backgrounds reduce to original plus Minkowski space via coordinate change.

Contraction leads to Nappi--Witten algebra and non-factorized geometry.

All D-branes survive the Penrose limit, enabling analysis of plane wave backgrounds.

Abstract

We study exact string backgrounds (WZW models) generated by nonsemisimple algebras which are obtained as double extensions of generic D--dimensional semisimple algebras. We prove that a suitable change of coordinates always exists which reduces these backgrounds to be the product of the nontrivial background associated to the original algebra and two dimensional Minkowski. However, under suitable contraction, the algebra reduces to a Nappi--Witten algebra and the corresponding spacetime geometry, no more factorized, can be interpreted as the Penrose limit of the original background. For both configurations we construct D--brane solutions and prove that {\em all} the branes survive the Penrose limit. Therefore, the limit procedure can be used to extract informations about Nappi--Witten plane wave backgrounds in arbitrary dimensions.