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

As a step toward uncovering the relation between the weak and the strong coupling regimes of the N = 4 super Yang-Mills theory beyond the spectral level, we have developed in a previous paper (arXiv:1410.8533) a novel group theoretic interpre- tation of the Wick contraction of the fields, which allowed us to compute a much more general class of three-point functions in the SU(2) sector, as in the case of strong coupling (arXiv:1312.3727), directly in terms of the determinant representation of the partial domain wall partition function. Furthermore, we derived a non-trivial identity for the three point functions with monodromy operators inserted, being the discrete counterpart of the global monodromy condition which played such a crucial role in the computation at strong cou- pling. In this companion paper, we shall extend our study to the entire psu(2,2|4) sector and obtain several important generalizations. They include in particular (i) the manifestly conformally covariant construction, from the basic principle, of the singlet-projection oper- ator for performing the Wick contraction and (ii) the derivation of the monodromy relation for the case of the so-called "harmonic R-matrix", as well as for the usual fundamental R- matrtix. The former case, which is new and has features rather different from the latter, is expected to have important applications. We also describe how the form of the monodromy relation is modified as psu(2,2|4) is reduced to its subsectors.