set of pp-wave s (one for each point of the parameter space). We refer to them as to *rotated pp-wave backgrounds*.

Note that the backgrounds obtained in this way do not necessarily have any specific meaning in an AdS/CFT context. They will only have a meaning in the AdS/CFT context if we derive them from a Penrose limit of $\mbox{AdS}_5 \times S^5$. Despite this, the procedure that we are going to show results to be very useful because allows to obtain a general formula that contains all the physically interesting pp-wave s. In fact we will show that by appropriately choosing the values of the parameters of the background, this general formula describes exactly the s studied in the previous section which are indeed obtained by taking Penrose limits of the $\mbox{AdS}_5 \times S^5$ .

We can then proceed in finding the spectra on these generic rotated s. An important result is that, by taking an appropriate limit on these spectra, we will show that one can reproduce the spectra found in [@Harmark:2007px] for the nine decoupled sectors of $\neqf$ SYM which contain scalars.

Coordinate transformation
-------------------------

We start from the simplest pp-wave background metric without flat directions $$\label{BMNmetric}
ds^2=-4dx^+dx^- 