Perturbative four-point functions in planar $$ \mathcal{N}=4 $$ SYM From hexagonalization

Abstract

Abstract We use hexagonalization to compute four-point correlation functions of long BPS operators with special R-charge polarizations. We perform the computation at weak coupling and show that at any loop order our correlators can be expressed in terms of single value polylogarithms with uniform and maximal transcendentality. As a check of our computation we extract nine-loop OPE data and compare it against sum rules of (squared) structures constants of non-protected exchanged operators described by hundreds of Bethe solutions.