  We derive a product rule satisfied by restricted Schur polynomials. We focus
mostly on the case that the restricted Schur polynomial is built using two
matrices, although our analysis easily extends to more than two matrices. This
product rule allows us to compute exact multi-point correlation functions of
restricted Schur polynomials, in the free field theory limit. As an example of
the use of our formulas, we compute two point functions of certain single trace
operators built using two matrices and three point functions of certain
restricted Schur polynomials, exactly, in the free field theory limit. Our
results suggest that gravitons become strongly coupled at sufficiently high
energy, while the restricted Schur polynomials for totally antisymmetric
representations remain weakly interacting at these energies. This is in perfect
accord with the half-BPS (single matrix) results of hep-th/0512312. Finally, by
studying the interaction of two restricted Schur polynomials we suggest a
physical interpretation for the labels of the restricted Schur polynomial: the
composite operator $\chi_{R,(r_n,r_m)}(Z,X)$ is constructed from the half BPS
``partons'' $\chi_{r_n}(Z)$ and $\chi_{r_m}(X)$.

High Energy Physics - Theory