On Four-Point Functions of Half-BPS Operators in General Dimensions

We study four-point correlation functions of ½-BPS operators of arbitrary weight for all dimensions d = 3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d = 4, where in addition functions of a single variable appear. We also discuss the operator product expansion using recent results on conformal partial wave amplitudes in arbitrary dimension.