Generalized complex marginal deformation of pp-waves and giant gravitons

We present the Penrose limits of a complex marginal deformation of $AdS_5times S^5$, which incorporates the $SL(2,mathbb{R})$ symmetry of type IIB theory, along the $(J,0,0)$ geodesic and along the $(J,J,J)$ geodesic. We discuss giant gravitons on the deformed $(J,0,0)$ pp-wave background.