Universal properties of superconformal OPEs for 1/2 BPS operators in 3⩽D⩽6

We give a general analysis of OPEs of 1/2 BPS superfield operators for the D = 3, 4, 5, 6 superconformal algebras OSp(8/4, R), PSU(2, 2/4), F4 and OSp(8*/4) which underlie maximal AdS supergravity in 4 ⩽ D + 1 ⩽ 7. The corresponding three-point functions can be formally factorized in a way similar to the decomposition of a generic superconformal UIR into a product of supersingletons. This allows for a simple derivation of branching rules for primary superfields. The operators of protected conformal dimension which may appear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, or semishort. As an application, we discuss the `non-renormalization' of extremal n-point correlators.