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Form factors, as quantities involving both local operators and asymptoticparticle states, contain information of both the spectrum of operators and theon-shell amplitudes. So far the studies of form factors have been mostlyfocused on the large Nc planar limit, with a few exceptions of Sudakov formfactors. In this paper, we discuss the systematical construction of full colordependent form factors with generic local operators. We study the colordecomposition for form factors and discuss the general strategy of usingon-shell unitarity cut method. As concrete applications, we compute the fulltwo-loop non-planar minimal form factors for both half-BPS operators andnon-BPS operators in SU(2) sector in N=4 SYM. Another important aspect is toinvestigate the color-kinematics (CK) duality for form factors with high-lengthoperators. Explicit CK dual representation is found for the two-loop half-BPSminimal form factors with arbitrary number of external legs. The full-colortwo-loop form factor results provide an independent check of the infrareddipole formula for two-loop n-point amplitudes. By extracting the UVdivergence, we also reproduce the known two-loop non-planar SU(2) dilatationoperator. As for the finite remainder function, interestingly, the non-planarpart is found to contain a new maximally transcendental part beyond the knownplanar result.

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality