Four-point functions of different-weight operators in the AdS/CFT correspondence

We calculate four-point correlation functions of two weight-2 and two weight-3 ½-BPS operators in Script N = 4 SYM in the large N limit in supergravity approximation. By the AdS/CFT conjecture, these operators are dual to AdS5; supergravity scalar fields s2 and s3 with mass m2 = −4 and m2 = −3 respectively. This is the first non-trivial four-point function of mixed-weight operators of lowest conformal dimensions. We show that the supergravity-induced four-point function splits into a ``free" and a ``quantum" part, where the quantum contribution obeys non-trivial constraints coming from the insertion procedure in the gauge theory, in particular, it depends on only one function of the conformal cross-ratios