go well beyond the planar limit; we find the methods and approach of[@Balasubramanian:2004nb; @de; @Mello; @Koch:2007uu; @de; @Mello; @Koch:2007uv; @Kimura:2007wy; @Bekker:2007ea; @Brown:2007xh; @Bhattacharyya:2008rb; @Brown:2008rr; @Kimura:2008wy; @Kimura:2009wy] once again surprisingly effective. The results again exhibit a remarkable simplicity - the spectrum of anomalous dimension can be matched to the spectrum of a set of oscillators! We see once again that the large $N$ limit is indeed a simple limit.

The operators we consider, restricted Schur polynomials, will be built using $O(N)$ $Z$s and 3 or 4 “impurities” ($Y$s), where $Z$ and $Y$ are complex adjoint scalars of ${\cal N}=4$ super Yang Mills theory. The case of operators with two impurities was studied in[@Koch:2010gp]. The dilatation operator when acting on a restricted Schur polynomial, produces terms that have a combination $ZY-YZ$ appearing. In [@Koch:2010gp], the techniques of [@de; @Mello; @Koch:2007uv; @Bekker:2007ea] were used to separate the $Z$ and the $Y$ and then write the results as a linear combination of restricted Schur polynomials. This method is very cumbersome as it involves the inversion of a matrix. This must be done analytically so its tedious (for the case of two impurities one must invert a $6\times 6$ matrix). More than two impurities was 