Field theory tests for correlators in the AdS-CFT correspondence

The order $g^2$ radiative corrections to all two- and three-point correlators of the composite primary operators $\mathrm{Tr}{X}^k$ are computed in $\mathcal{N}=4\mathrm{}$ supersymmetric Yang-Mills theory with the gauge group $\mathrm{SU}\mathrm{}\left(N\right).$ Corrections are found to vanish for all $N.\mathrm{}$ For $k=2\mathrm{}$ this is a consequence of known superconformal nonrenormalization theorems, and for general $k$ the result confirms an $\overrightarrow{N}\infty ,$ fixed large $g^{2}N$ supergravity calculation and further conjectures by S. Lee et al., hep-th/9806074. A three-point correlator involving $\mathcal{N}=4\mathrm{}$ descendents of $\mathrm{Tr}{X}^2$ is calculated, and its order $g^2$ contribution also vanishes, giving evidence for the absence of radiative corrections in correlators of descendent operators.