Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory

TL;DR

This paper constructs the complete five-loop integrand of the Sudakov form factor in N=4 super-Yang-Mills theory using color-kinematics duality, revealing non-planar contributions and implications for ultraviolet finiteness.

Contribution

First explicit five-loop integrand of the Sudakov form factor in N=4 SYM including non-planar parts, demonstrating color-kinematics duality at this loop order.

Findings

Integrand is ultraviolet finite for D<26/5.

First manifestation of color-kinematics duality at five loops.

Potential implications for N=8 supergravity finiteness.

Abstract

Using color-kinematics duality, we construct for the first time the full integrand of the five-loop Sudakov form factor in N=4 super-Yang-Mills theory, including non-planar contributions. This result also provides a first manifestation of the color-kinematics duality at five loops. The integrand is explicitly ultraviolet finite when D<26/5, coincident with the known finiteness bound for amplitudes. If the double-copy method could be applied to the form factor, this would indicate an interesting ultraviolet finiteness bound for N=8 supergravity at five loops. The result is also expected to provide an essential input for computing the five-loop non-planar cusp anomalous dimension.