were found in the case of the planar limit using the idea of integrability and the connection to spin chains [@Minahan:2002ve; @Beisert:2003tq; @Beisert:2003yb][^1] particularly by considering a near plane wave limit with curvature corrections to the pp-wave background [@Callan:2003xr; @Callan:2004uv]. A high point of this is the development of the Asymptotic Bethe Ansatz describing the dimension of infinitely long operators for any ’t Hooft coupling in the planar limit [@Staudacher:2004tk; @Beisert:2005tm; @Beisert:2006ez]. Going beyond the planar limit seems instead to be very difficult [@Kristjansen:2002bb]. New ideas are needed in order to further explore the AdS/CFT correspondence in the non-planar limit and its potential applications.

Recently another example of an exact duality between ${\mathcal{N}}= 6$ superconformal Chern-Simons theory (ABJM theory) and type IIA string theory on $\mbox{AdS}_4 \times CP^3$ have been found [@Aharony:2008ug]. Also here certain Penrose limits and near plane wave limits have been explored [@Nishioka:2008gz; @Gaiotto:2008cg; @Grignani:2008is; @Astolfi:2008ji; @Astolfi:2009qh].

The difficulty of going beyond the planar limit, where integrability most likely is absent, makes it desirable to consider alternative approaches to match the spectrum of operators and string states. One of the cornerstones in comparing the operator spectrum to the string spectrum in a Penrose limit or near-plane wave 