Mashile, Grant2011-05-252011-05-252011-05-25http://hdl.handle.net/10539/9923In this dissertation we study the anomalous dimension of operators with Rcharge of order N in the ’t Hooft limit. This is a highly non-trivial task as the planar approximation, which is usually used to simplify the problem, is not accurate. One is forced to sum all Feynman diagrams. The operators of interest are dual to a system of two excited giant gravitons. We build the Yang Mills operators using restricted Schur polynomials that are labeled by Young diagrams that have at most two columns. We learn from our analysis that the giant gravitons behave as a two coupled harmonic oscillators.enThesis