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

TL;DR

This paper computes three-point functions in N=4 SYM and compares them with three-string interactions in pp-wave backgrounds, confirming the AdS/CFT correspondence at subleading order.

Contribution

It provides the first all-orders prediction for field theory three-point functions and matches them with string theory results at subleading order.

Findings

Exact expressions for Neumann matrices to all orders.

Agreement between field theory and string theory results at subleading order.

First all-orders prediction for three-point functions in this context.

Abstract

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.