All three-loop four-point correlators of half-BPS operators in planar N=4 SYM

International audienceWe obtain the planar correlation function of four half-BPS operators ofarbitrary weights, up to three loops. Our method exploits only elementaryproperties of the integrand of the planar correlator, such as its symmetriesand singularity structure. This allows us to write down a general ansatz forthe integrand. The coefficients in the ansatz are fixed by means of a powerfullight-cone OPE relation between correlators with different weights. Our resultis formulated in terms of a limited number of functions built from known one-,two- and three-loop conformal integrals. These results are useful for checkingrecent integrability predictions for the OPE structure constants