Ambient Metrics for n-Dimensional pp-Waves

We provide an explicit formula for the Fefferman-Graham ambient metric of an n -dimensional conformal pp -wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all 4-dimensional pp -waves that are Bach-flat, and give a large class of Bach-flat examples which are conformally Cotton-flat, but not conformally Einstein. Finally, as an application, we use the obtained ambient metric to show that even-dimensional pp -waves have vanishing critical Q -curvature.