Tessellating cushions: four-point functions in N=4 SYM

TL;DR

This paper introduces a novel tessellation approach to compute planar four-point functions in N=4 SYM, using modified hexagon form-factors, potentially offering an integrability-based alternative to traditional methods.

Contribution

It presents a new tessellation method for four-point functions in N=4 SYM, connecting planar diagrams with modified hexagon form-factors, independent of the OPE framework.

Findings

Each tile corresponds to a modified hexagon form-factor.

The tessellation efficiently reproduces tree-level four-point functions.

The approach is not based on the OPE, suggesting a new integrability-based method.

Abstract

We consider a class of planar tree-level four-point functions in N=4 SYM in a special kinematic regime: one BMN operator with two scalar excitations and three half-BPS operators are put onto a line in configuration space; additionally, for the half-BPS operators a co-moving frame is chosen in flavour space. In configuration space, the four-punctured sphere is naturally triangulated by tree-level planar diagrams. We demonstrate on a number of examples that each tile can be associated with a modified hexagon form-factor in such a way as to efficiently reproduce the tree-level four-point function. Our tessellation is not of the OPE type, fostering the hope of finding an independent, integrability-based approach to the computation of planar four-point functions.