limit is that in comparing the spectrum of operators one assumes that most of the operators of the gauge theory receive an infinitely large correction to the bare dimension in the large ’t Hooft coupling limit $\lambda \rightarrow \infty$. This is of course a built in feature of the Asymptotic Bethe Ansatz for ${\mathcal{N}}=4$ SYM. However, an alternative approach to this problem of taking the strong coupling limit of ${\mathcal{N}}=4$ SYM has been proposed in [@Harmark:2006di; @Harmark:2006ta; @Harmark:2006ie; @Harmark:2007et; @Harmark:2007px; @Harmark:2008gm] where a regime of AdS/CFT was found in which both gauge theory and string theory are reliable and the correspondence can be tested in a precise way.

Applying the approach of [@Harmark:2006di; @Harmark:2006ta; @Harmark:2006ie; @Harmark:2007et; @Harmark:2007px; @Harmark:2008gm][^2] to match the spectrum of operators and string states in the $SU(2)$ sector uses in an essential way the alternative Penrose limit of [@Bertolini:2002nr] where the maximally supersymmetric pp-wave has an explicit isometry. This is because for this pp-wave background the string states having an energy just above the vacuum energy are the states dual to the operators in the $SU(2)$ sector of ${\mathcal{N}}=4$ SYM.

However, as shown in [@Harmark:2007px] there are several other sectors of ${\mathcal{N}}=4$ SYM that one can explore 