able to distinguish (for example) giant graviton plus graviton from excited giant graviton. Our study captures only states of the two giant system. Thus, it is rather natural to associate our oscillators with excitations modes of a giant graviton. [*In the same way that there are oscillators in the worldsheet theory of a string describing the oscillation modes of a string, we are describing the oscillators that would be present in a world volume description of giant gravitons describing the oscillations modes of a giant graviton D3 brane.*]{}

The problem of computing anomalous dimensions for operators with a large ${\cal R}$-charge has been considered before by a number of authors. The restricted Schur polynomials we consider in this article are built by distributing “impurities” (given by $Y$s), in an operator built mainly from $Z$s. If we replace the $Y$s by words containing $O(\sqrt{N})$ letters (which may be $Z$, $Y$ or other field or derivative of a field), these words are naturally identified with open strings[@Balasubramanian:2002sa; @Sadri:2003mx; @Berenstein:2003ah]. In this case the dilatation operator reproduces the dynamics of open strings ending on a giant graviton[@Berenstein:2006qk; @de; @Mello; @Koch:2007uu; @de; @Mello; @Koch:2007uv; @Bekker:2007ea]. The mixing of operators is highly constrained. Indeed, in 