We denote generating functions of massless even higher-spin fields "primitive string fields"(PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher-spin field theories in AdS d+1 are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for 1 ≤ N ≤∞ play for us the role of "standard models", for varying N, they contain, e. g., the Ising model for N = 1 and the spherical model for N = ∞. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal(quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s ≥ 4, they are distinguished by their anomalous dimensions(in CFT _3) or by theirmass(in AdS _4). We sum over these multiplets and the spins to obtain "string type fields", one for each such monomial.
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