Field theory tests for correlators in the AdS-CFT correspondence

Abstract

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 $\mathcal{N}=4$ supersymmetric Yang-Mills theory with the gauge group $\mathrm{SU}(N).$ Corrections are found to vanish for all $N.$ For $k=2$ this is a consequence of known superconformal nonrenormalization theorems, and for general $k$ the result confirms an $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ fixed large ${g}^{2}N$ supergravity calculation and further conjectures by S. Lee et al., hep-th/9806074. A three-point correlator involving $\mathcal{N}=4$ 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.