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

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.

arXiv comment6 pages, 6 figures; v2, auxiliary file with three-parameter numerators provided, references added, minor changes, published version

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• Type D Spacetimes and the Weyl Double Copy
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Gravity Amplitudes as Generalized Double Copies
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• A Three-Point Form Factor Through Five Loops
• Off-Shell Color-Kinematics Duality for Chern-Simons
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Unraveling conformal gravity amplitudes
• UV considerations on scattering amplitudes in a web of theories
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Full-color three-loop three-point form factors in N=4 SYM
• Kinematic Hopf algebra for amplitudes and form factors
• On Form Factors and Correlation Functions in Twistor Space
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
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