  The metric of a spacetime with a parallel plane (pp)-wave can be obtained in
a certain limit of the space AdS^5xS^5. According to the AdS/CFT
correspondence, the holographic dual of superstring theory on that background
should be the analogous limit of N=4 supersymmetric Yang-Mills theory. In this
paper we shall show that, contrary to widespread expectation, non-planar
diagrams survive this limiting procedure in the gauge theory. Using matrix
model techniques as well as combinatorial reasoning it is demonstrated that a
subset of diagrams of arbitrary genus survives and that a non-trivial double
scaling limit may be defined. We exactly compute two- and three-point functions
of chiral primaries in this limit. We also carefully study certain operators
conjectured to correspond to string excitations on the pp-wave background. We
find non-planar linear mixing of these proposed operators, requiring their
redefinition. Finally, we show that the redefined operators receive non-planar
corrections to the planar one-loop anomalous dimension.
