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We find an asymptotic solution for two- and three-point correlators of localgauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$,in terms of glueball and meson propagators, by means of a new purelyfield-theoretical technique that we call the asymptotically-free bootstrap. Theasymptotically-free bootstrap exploits the lowest-order conformal invariance ofconnected correlators of gauge invariant composite operators in perturbationtheory, the renormalization-group improvement, and a recently-proved asymptoticstructure theorem for glueball and meson propagators, that involves the unknownparticle spectrum and the anomalous dimension of operators for fixed spin. Inprinciple the asymptotically-free bootstrap extends to all the higher-spin two-and three-point correlators whose lowest-order conformal limit is non-vanishingin perturbation theory, and by means of the operator product expansion to thecorresponding asymptotic multi-point correlators as well. Besides, theasymptotically-free bootstrap provides asymptotic $S$-matrix amplitudes inmassless large-$N$ $QCD$ in terms of glueball and meson propagators as opposedto perturbation theory. Remarkably, the asymptotic $S$-matrix depends only onthe unknown particle spectrum, but not on the anomalous dimensions. Moreover,the asymptotically-free bootstrap applies to large-$N$ $\mathcal{N}=1$ $SUSY$$YM$ as well. Practically, as just a few examples among many more, it followsthe structure of the light by light scattering amplitude, of the pion formfactor, and the associated vector dominance. Theoretically, the asymptoticsolution sets the strongest constraints on any actual solution of large-$N$$QCD$ (and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$), and in particular on anystring solution.

An asymptotic solution of large-$N$ $QCD$, and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$