Park, Nicholas Joseph2010-09-082010-09-082010-09-08http://hdl.handle.net/10539/8626We use the duality between Schur polynomials and half BPS operators in order to diagonalize the one loop dilatation operator studied in [1] and [2]. This problem has been studied for operators with R-charge of O(1) and O(√N), corresponding to Kaluza-Klein gravitons and strings respectively. Due to the complexity of the problem, there has been no prior attempt to study the problem with R-charge of O(N) corresponding to D-branes solutions. In this work we study a large N limit where a particular sector decouples. This sector corresponds to two nearly maximal spherical giant gravitons.enThesis