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arXiv · 2106.05280

Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations

Guanda Lin·Gang Yang·Siyuan Zhang
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Abstract

We obtain full-color three-loop three-point form factors of the stress-tensor supermultiplet and also of a length-3 half-BPS operator in N=4 SYM based on the color-kinematics duality and on-shell unitarity. The integrand results are verified by all planar and non-planar unitarity cuts, and they satisfy the minimal power-counting of loop momenta and diagrammatic symmetries. Interestingly, these three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of stress-tensor supermultiplet. Such degrees of freedom are due to a new type of generalized gauge transformation associated with the operator insertion for form factors. We also perform numerical integration and obtain consistent full-color infrared divergences and the known planar remainder. The form factors we obtain can be understood as the N=4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and are expected to provide the maximally transcendental parts of the latter.

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Guanda Lin, Gang Yang, Siyuan Zhang. 2021-06-09. Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations. https://doi.org/10.1103/physrevlett.127.171602

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