Color-kinematics duality and dual conformal symmetry for a four-loop form factor in \(\mathcal{N}\) = 4 SYM

We obtain the integrand of full-color four-loop three-point form factor of the stress-tensor supermultiplet in \(\mathcal{N}\) $\mathcal{N}$ = 4 SYM, based on the color-kinematics (CK) duality and generalized unitarity method. Our result not only manifests all dual Jacobi relations via CK duality but also contains 133 free parameters. This suggests the constructibility of the form factor at even higher loops via CK duality. We also find that the planar form factor has a hidden dual conformal symmetry in the lightlike limit of the operator momentum, which is checked up to four loops.