UC Santa Barbara

In the last few years, there has been a surge of interest in studying the AdS/CFT duality through the generating functions for half and quarter BPS correlators in N = 4 SYM theory. We arrive at these functions through representation theory; while the required calculations usually involve combinatorics and are computationally tedious, an exact formula-- and in the case of quarter BPS correlators, an exact formula for the gauge group SU(2) and a prescription for arriving at a more generic formula for N>2-- can be found through the application of the Harish-Chandra-Itzykson-Zuber integral formula, which makes use of the localization theorem. This thesis focuses on developing the mathematical tools needed to probe AdS giant gravitons and their interpretations as BPS coherent states.