A dyeing procedure maps form factors to colored amplitudes, recovering the originals by bleaching and explaining double-copy features through standard BCJ relations.
Yang,Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory,Phys
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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.
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Determines the unique two- and three-loop symbols for the four-point NMHV form factor from an 88-letter alphabet, providing first multi-loop non-MHV data and supporting alphabet universality.
The chiral algebra bootstrap yields all-loop splitting functions for self-dual N=4 SYM, a proof of no double-pole OPEs, and novel two-loop form factors with anti-self-dual field strength insertions.
A dyeing procedure generalizes the double copy to form factors with multiple operator insertions by mapping spurious poles to physical propagators and revealing a new scalar-ordering structure in gravity.
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