Exact correlators of giant gravitons from dual $N = 4$ SYM theory

A class of correlation functions of half-BPS composite operators are computed exactly ( at finite JV ) in the zero coupling limit of iV = 4 SYM theory. These have a simple dependence on the fourdimensional spacetime coordinates and are related to correlators in a one-dimensional Matrix Model with complex Matrices obtained by dimensional reduction of iV = 4 SYM on a three-sphere. A key technical tool is Frobenius-Schur duality between symmetric and Unitary groups and the results are expressed simply in terms of U(N) group integrals or equivalently in terms of Littlewood-Richardson coefficients. These correlation functions are used to understand the existence/properties of giant gravitons and related solutions in the string theory dual on AdSs x 5 5 . Some of their properties hint at integrability in N = 4 SYM.