Higher-point correlators in 𝒩 = 4 SYM: ten-dimensional null polygons

A bstract We consider higher-point generalizations of the “octagon” large-charge four-point function in planar 𝒩 = 4 super Yang-Mills theory. These n -point polygon correlators are defined as ten-dimensional null limits of generating functions of n -point correlators of protected scalar operators with arbitrary R-charge, and are conjecturally dual to massive scattering amplitudes of W-bosons on the Coulomb branch of the theory. We present a twistor-based direct computation of the polygon loop integrands, and determine the two-loop integrands for any number of external operators. The result is expressed as a linear combination of conformal integrals, with coefficients that are rational functions of the spacetime distances and operator polarizations. We obtain an exact match with a one-loop integrability computation, and study the near-massless limit of the pentagon function.