the quadratic potential terms for the transverse directions are massive for all eight transverse directions. Another coordinate system was introduced in [@Michelson:2002wa; @Bertolini:2002nr] and we will refer to it as the [*one flat direction pp-wave background*]{} due to the presence of a space-like isometry in the pp-wave metric and since in this case the quadratic terms for the transverse directions have a massless direction.

Here we find a new pp-wave background corresponding to a new coordinate system for the maximally supersymmetric pp-wave of type IIB supergravity. This new background is again obtained as a Penrose limit of $\mbox{AdS}_5 \times S^5$ with an appropriate choice of light-cone coordinates. The new pp-wave background differs from the other two because of the presence of two spacial isometries in the metric, namely two flat directions, corresponding to two massless directions in the potential terms for the transverse directions. Hence we call it the [*two flat directions pp-wave background*]{}.

This new pp-wave background is important in the context of the AdS/CFT correspondence. In fact, as shown explicitly in Section \[sec:stringrotspectra\], string theory can be quantized on this background. Moreover, as discussed in Section \[sec:decsectors\], after taking a certain limit on the spectrum of type IIB 