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

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