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In the context of the $AdS_{4}/CFT_{3}$ correspondence between higher spinfields and vector theories, we use the constructive bilocal fields basedapproach to this correspondence, to demonstrate, at the $IR$ critical point ofthe interacting vector theory and directly in the bulk, the removal of the$\Delta=1$ ($s=0$) state from the higher spins field spectrum, and to exhibitsimple Klein-Gordon higher spin Hamiltonians. The bulk variables and higherspin fields are obtained in a simple manner from boundary bilocals, by thechange of variables previously derived for the $UV$ critical point (in momentumspace), together with a field redefinition.

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