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

Understand

As a step toward uncovering the relation between the weak and the strong coupling regimes of the $\mathcal{N}=4$ super Yang-Mills theory beyond the specral level, we have developed in a previous paper [arXiv:1410.8533] a novel group theoretic interpretation 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 funciton.

• 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 coupling.
• In this companion paper, we shall extend our study to the entire ${\rm psu}(2,2|4)$ sector and obtain several important generalizations.
• They include in particular (i) the manifestly conformally covariant construction, from the basic principle, of the singlet-projection operator 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.