Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM4

We study perturbative and instanton corrections to the Operator Product Exp ansion of the lowest weight Chiral Primary Operators of N = 4 SYM4. We conf irm the recently observed nonrenormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), th at appear to be unprotected by unitarity restrictions. We demonstrate the s plitting of the free-field theory stress tenser and R-symmetry current in s upermultiplets acquiring different anomalous dimensions in perturbation the ory and argue that certain double-trace operators also undergo a perturbati ve splitting into operators dual to string and two-particle gravity states, respectively. The instanton contributions affect only those double-tract o perators that acquire finite anomalous dimensions at strong coupling. For t he leading operators of this kind, we show that the ratio of their anomalou s dimensions at strong coupling to the anomalous dimensions due to instanto ns is the same number. (C) 2001 Published by Elsevier Science B.V.