Exact Correlators of Giant Gravitons from dual N=4 SYM

TL;DR

This paper computes exact correlation functions of half-BPS operators in N=4 SYM at finite N, revealing insights into giant gravitons and suggesting possible integrability in the theory.

Contribution

It provides a novel exact computation of correlators using Frobenius-Schur duality and group integrals, connecting gauge theory results to string theory duals.

Findings

Exact correlators depend simply on spacetime coordinates

Results relate to matrix models and group integrals

Hints at integrability in N=4 SYM

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 $ AdS_5 \times S^5$. Some of their properties hint at integrability in N=4 SYM.