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

Abstract

A class of correlation functions of half-BPS composite operators are computed exactly ( at finite N ) in the zero coupling limit of N = 4 SYM theory. These have a simple dependence on the four-dimensional spacetime coordinates and are related to correlators in a one-dimensional Matrix Model with complex Matrices obtained by dimensional reduction of N = 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 AdS5 × S5. Some of their properties hint at integrability in N = 4 SYM.