String Theory on Parallelizable PP-Waves

TL;DR

This paper classifies and analyzes parallelizable pp-wave backgrounds in string theory, exploring their supersymmetry, T-duality invariance, and implications for string quantization and D-branes.

Contribution

It provides a comprehensive classification of parallelizable pp-wave backgrounds, their supersymmetry properties, T-duality invariance, and studies string quantization and D-branes in these backgrounds.

Findings

Parallelizable pp-waves are homogeneous plane-waves.

They preserve varying amounts of supersymmetry, up to 28 supercharges.

These backgrounds are invariant under T-duality, with potential changes in supersymmetry.

Abstract

The most general parallelizable pp-wave backgrounds which are non-dilatonic solutions in the NS-NS sector of type IIA and IIB string theories are considered. We demonstrate that parallelizable pp-wave backgrounds are necessarily homogeneous plane-waves, and that a large class of homogeneous plane-waves are parallelizable, stating the necessary conditions. Such plane-waves can be classified according to the number of preserved supersymmetries. In type IIA, these include backgrounds preserving 16, 18, 20, 22 and 24 supercharges, while in the IIB case they preserve 16, 20, 24 or 28 supercharges. An intriguing property of parallelizable pp-wave backgrounds is that the bosonic part of these solutions are invariant under T-duality, while the number of supercharges might change under T-duality. Due to their \alpha' exactness, they provide interesting backgrounds for studying string theory. Quantization of string modes, their compactification and behaviour under T-duality are studied. In addition, we consider BPS $Dp$-branes, and show that these $Dp$-branes can be classified in terms of the locations of their world volumes with respect to the background $H$-field.