AdS pp-waves

TL;DR

This paper derives pp-wave solutions in various gauged supergravity theories, analyzing their supersymmetry properties and conditions for enhanced supersymmetry, including independence from certain coordinates.

Contribution

It provides explicit pp-wave solutions in D=5 and D=4 gauged supergravities with specific gauge fields and explores conditions for supersymmetry enhancement.

Findings

Most solutions preserve 1/4 supersymmetry.

Supernumerary supersymmetry occurs under specific harmonic function constraints.

Solutions are independent of the light-cone coordinate $x^+$.

Abstract

We obtain the pp-waves of D=5 and D=4 gauged supergravities supported by $U(1)^3$ and $U(1)^4$ gauge field strengths respectively. We show that generically these solutions preserve 1/4 of the supersymmetry, but supernumerary supersymmetry can arise for appropriately constrained harmonic functions associated with the pp-waves. In particular it implies that the solutions are independent of the light-cone coordinate $x^+$. We also obtain the pp-waves in the Freedman-Schwarz model.