Three-loop four-point correlator in N=4 SYM

Abstract We explicitly compute the complete three-loop (O( g 4 )) contribution to the four-point function of chiral primary current-like operators 〈 q 2 q 2 q 2 q 2 〉 in any finite N =2 SYM theory. The computation uses N =2 harmonic supergraphs in coordinate space. Dramatic simplifications are achieved by a double insertion of the N =2 SYM linearized action, and application of superconformal covariance arguments to the resulting nilpotent six-point amplitude. The result involves polylogarithms up to fourth order of the conformal cross ratios. It becomes particularly simple in the N =4 special case.