  Correlation functions of operators with a conformal dimension of O(N^2) are
not well approximated by the planar limit. The non-planar diagrams, which in
the bulk spacetime correspond to string loop corrections, are enhanced by huge
combinatorial factors. In this article we show how these loop corrections can
be resummed. As a typical example of our results, in the half-BPS background of
M maximal giant gravitons we find the usual 1/N expansion is replaced by a
1/(M+N) expansion. Further, we find that there is a simple exact relationship
between amplitudes computed in the trivial background and amplitudes computed
in the background of M maximal giant gravitons. Finally, we also find strong
evidence for the BMN-type sectors suggested in arXiv:0801.4457. The decoupling
limit of arXiv:0801.4457 captures the decoupled low energy world volume theory
of the intersecting giant graviton system and this theory is weakly coupled
even when the original N=4 super Yang-Mills theory is strongly coupled.
