  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.
