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Abstract

We study a class of non-protected local composite operators which emerge in the $SU(4)$-singlet channel of the OPE between two lowest dimension CPOs in ${cal N}=4$ SYM. These are quadrilinear operators which, in the free field limit, appear as double--trace color structures. When the interaction is turned on, a nontrivial mixing under renormalization occurs and they split in general into linear combinations of proper conformally invariant states which may involve both single and double traces. In a ${cal N}=1$ superspace setup we solve the mixing problem by computing the one-loop two point functions of all dimension 4 scalar operators, diagonalizing their anomalous dimension matrix and identifying the proper quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by $1/N^2$ with respect to the anomalous dimensions of the Konishi--like operators. We identify the mechanism underlying such a suppression and give an argument to prove its occurrence at every order in perturbation theory. We discuss our results in connection with the AdS/CFT correspondence which requires such operators to be dual to multi-particle supergravity states whose energy is less than the sum of the corresponding individual single-particle states