The maximally supersymmetric plane-wave backgrounds of IIB and eleven-dimensional supergravity share many properties is common with the Freund-Rubin backgrounds. One such property is the dimension of the symmetry superalgebra, a concept that I had previously elucidated geometrically in On the supersymmetries of anti de Sitter vacua. Not just were the superalgebras equidimensional, but in fact those of the plane waves were contractions of those of the Freund-Rubin backgrounds. This suggested that one could obtain these plane waves as geometric limits of the Freund-Rubin backgrounds.
Perusing the literature we came across the paper of Rahmi Güven on the plane-wave limit and T-duality, which extended to supergravity theories an earlier observation of Roger Penrose in the context of general relativity, namely that every lorentzian manifold has a plane wave as a geometric limit. With such a strong hint, it was not long until we exhibited our new plane-wave solution as the Penrose-Güven limit of the AdS5 x S5 background of IIB supergravity, and similarly for the eleven-dimensional backgrounds — results which were reported in Penrose limits and maximal supersymmetry.
According to the gauge/gravity correspondence there is a duality between string theory on backgrounds asymptotic to AdS5 x S5 and a conformal gauge field theory on the conformal boundary. Taking this duality at face value, one is forced to conclude that any stringy process must be reflected in the gauge theory, and viceversa. The plane-wave limit is no exception. David Berenstein, Juan Maldacena and Horatiu Nastase implemented the plane-wave limit in the gauge theory side and in the process discovered a novel large N limit of the gauge theory different from the one discovered by 't Hooft. It has the virtue that in this limit both the string theory and the gauge theory can be kept weakly coupled, at the price of focusing on a particular class of observables. This has allowed many perturbative checks of the gauge/gravity correspondence. Given the interest in this topic, it was felt that a more detailed study of the plane wave limit and its properties was needed and together with Matthias Blau and George Papadopoulos we wrote Penrose limits, supergravity and brane dynamics, which also contains a number of examples and classifications of possible plane-wave limits of several highly symmetric backgrounds.
In that paper we also paid close attention to those geometric properties which are inherited by the plane-wave limit. We show in particular that supersymmetries (including symmetries) always survive the plane-wave limit, which explains conceptually the existence of the maximally supersymmetric plane waves. Surprisingly, as illustrated by Christophe Patricot, homogeneity is one property which is not necessarily inherited under the plane-wave limit. My student Simon Philip has looked into this issue and has proved a theorem stating that the plane-wave limit along a homogeneous geodesic is homogeneous, whence in particular the plane-wave limit of a naturally reductive homogeneous space is always homogeneous.