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

TL;DR

This paper computes all five-loop planar four-point functions of half-BPS operators in N=4 SYM, using integrability and light-cone OPE constraints to fix the correlators and extract OPE data.

Contribution

It provides the first complete five-loop planar four-point correlators in N=4 SYM, including novel predictions for triple wrapping corrections in hexagon form factors.

Findings

All five-loop planar four-point functions obtained.

OPE coefficients extracted from correlators.

Prediction for triple wrapping correction at five loops.

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.