Demystifying the twistor construction of composite operators in $N=4$ super-Yang–Mills theory

We explain some details of the construction of composite operators in $N=4$ SYM that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC) superspace. We give a step-by-step elementary derivation and show that the result coincides with the recent hypothesis put forward in (arXiv:1603.04471) within the twistor approach. We provide the appropriate LHC-to-twistors dictionary. (paper)