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

Abstract

We obtain all planar four-point correlators of half-BPS operators in $\mathcal{N}=4$ SYM up to five loops. The ansatz for the integrand is fixed partially by imposing light-cone 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.

26 pages, 3 figures; ancillary files with results. v2: Published version and corrected typo in triple wrapping result. v3: Corrected error in citations from v2