Three-point functions in N=4 Yang-Mills theory and pp-waves

Recently it has been proposed that the coefficient of the three-point function of the BMN operators in N=4 supersymmetric Yang-Mills theory is related to the three-string interactions in the pp-wave background. We calculate three-point functions of these operators to the first order in the effective Yang-Mills coupling lambda' = g_{YM}^2 N/J^2 in planar perturbation theory. On the string theory side, we derive the explicit expressions of the Neumann matrices to all orders in 1/(\mu p^+ \alpha')^2. This allows us to compute the corresponding three-string scattering amplitudes. This provides an all orders prediction for the field theory three-point functions. We compare our field theory results with the string theory results to the subleading order in 1/(\mu p^+ \alpha')^2 and find perfect agreement.