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As a step toward uncovering the relation between the weak and the strongcoupling regimes of the $\mathcal{N}=4$ super Yang-Mills theory beyond thespecral level, we have developed in a previous paper [arXiv:1410.8533] a novelgroup theoretic interpretation of the Wick contraction of the fields, whichallowed us to compute a much more general class of three-point functions in theSU(2) sector, as in the case of strong coupling [arXiv:1312.3727], directly interms of the determinant representation of the partial domain wall partitionfunciton. Furthermore, we derived a non-trivial identity for the three pointfunctions with monodromy operators inserted, being the discrete counterpart ofthe global monodromy condition which played such a crucial role in thecomputation at strong coupling. In this companion paper, we shall extend ourstudy to the entire ${\rm psu}(2,2|4)$ sector and obtain several importantgeneralizations. They include in particular (i) the manifestly conformallycovariant construction, from the basic principle, of the singlet-projectionoperator for performing the Wick contraction and (ii) the derivation of themonodromy relation for the case of the so-called "harmonic R-matrix", as wellas for the usual fundamental R-matrtix. The former case, which is new and hasfeatures rather different from the latter, is expected to have importantapplications. We also describe how the form of the monodromy relation ismodified as ${\rm psu}(2,2|4)$ is reduced to its subsectors.

On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors