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

TL;DR

Using color-kinematics duality, the full integrand of the five-loop Sudakov form factor in N=4 super-Yang-Mills theory is constructed, including nonplanar contributions, for the first time.

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.

Figures (6)

• Figure 1: Cubic graphs for four-point tree amplitudes.
• Figure 2: Color-kinematics related graphs at loop level.
• Figure 3: Master graphs for the five-loop Sudakov form factor.
• Figure 4: Non-trivial unitarity cuts of five-loop form factor. Each blob denotes a tree amplitude or form factor.
• Figure 5: Unitarity check of subtle 1PR graphs.