All five-loop planar four-point functions of half-BPS operators in $$ \mathcal{N}=4 $$ SYM

Abstract

Abstract We obtain all planar four-point correlators of half-BPS operators in $$ \mathcal{N}=4 $$ N = 4 SYM up to five loops. The ansatz for the integrand is fixed partially by imposing lightcone OPE relations between different correlators. We then fix the integrated correlators by comparing their asymptotic expansions with simple data obtained from integrability. We extract OPE coefficients and find a prediction for the triple wrapping correction of the hexagon form factors, which contributes already at the five-loop order.