Correlators of short multitrace operators in N=4 supersymmetric Yang-Mills theory

Multitrace scalar operators in the $\mathrm{}(0,k,0)\mathrm{}$ representations of $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}_R$ share many properties with their single-trace analogues. These multitrace operators are primary fields of short representations of the $\mathcal{N}=4\mathrm{}$ superconformal group. Thus, they have protected dimensions. We show that two- and three-point correlator functions of such operators do not receive radiative corrections at order $g^2$ in perturbation theory for an arbitrary gauge group.