Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons

TL;DR

This paper explores higher-point correlators in N=4 SYM, providing explicit two-loop integrands for polygonal configurations, and establishes their connection to scattering amplitudes through twistor methods and integrability.

Contribution

It introduces a twistor-based method to compute n-point polygon loop integrands in N=4 SYM and derives explicit two-loop results for arbitrary external points.

Findings

Exact two-loop integrands expressed as conformal integrals.

Match with one-loop integrability computations.

Analysis of the near-massless limit of the pentagon function.

Abstract

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.