  We find an asymptotic solution for two- and three-point correlators of local
gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$,
in terms of glueball and meson propagators, by means of a new purely
field-theoretical technique that we call the asymptotically-free bootstrap. The
asymptotically-free bootstrap exploits the lowest-order conformal invariance of
connected correlators of gauge invariant composite operators in perturbation
theory, the renormalization-group improvement, and a recently-proved asymptotic
structure theorem for glueball and meson propagators, that involves the unknown
particle spectrum and the anomalous dimension of operators for fixed spin. In
principle the asymptotically-free bootstrap extends to all the higher-spin two-
and three-point correlators whose lowest-order conformal limit is non-vanishing
in perturbation theory, and by means of the operator product expansion to the
corresponding asymptotic multi-point correlators as well. Besides, the
asymptotically-free bootstrap provides asymptotic $S$-matrix amplitudes in
massless large-$N$ $QCD$ in terms of glueball and meson propagators as opposed
to perturbation theory. Remarkably, the asymptotic $S$-matrix depends only on
the unknown particle spectrum, but not on the anomalous dimensions. Moreover,
the asymptotically-free bootstrap applies to large-$N$ $\mathcal{N}=1$ $SUSY$
$YM$ as well. Practically, as just a few examples among many more, it follows
the structure of the light by light scattering amplitude, of the pion form
factor, and the associated vector dominance. Theoretically, the asymptotic
solution sets the strongest constraints on any actual solution of large-$N$
$QCD$ (and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$), and in particular on any
string solution.
