  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 [2],[3]. 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 $1\leq N \leq \infty$ 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 $N=\infty$. 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 $s \geq 4$, they are distinguished by
their anomalous dimensions (in $CFT_3$) or by their mass (in $AdS_4$). We sum
over these multiplets and the spins to obtain "string type fields", one for
each such monomial.
