Constructing the bulk at the critical point of three-dimensional large $N$ vector theories

In the context of the $Ad{S}_4\mathrm{/}CF{T}_3$ correspondence between higher spin fields and vector theories, we use the constructive bilocal fields based approach to this correspondence, to demonstrate, at the $IR$ critical point of the interacting vector theory and directly in the bulk, the removal of the $\mathrm{\Delta }=1$ ($s=0$) state from the higher spins field spectrum, and to exhibit simple Klein-Gordon higher spin Hamiltonians. The bulk variables and higher spin fields are obtained in a simple manner from boundary bilocals, by the change of variables previously derived for the $UV$ critical point (in momentum space), together with a field redefinition.