  We prove an asymptotic structure theorem for glueball and meson propagators
of any spin in large-N QCD and in n=1 SUSY QCD with massless quarks, that
determines asymptotically the residues of the poles of the propagators in terms
of their anomalous dimensions and of the spectral density of the masses. The
asymptotic theorem follows by the severe constraints on the propagators in
large-N QCD with massless quarks, or in any large-N confining
asymptotically-free gauge theory massless in perturbation theory, that arise by
perturbation theory in conjunction with the renormalization group and by the
OPE on the ultraviolet side. The asymptotic theorem is inspired by a recently
proposed Topological Field Theory (TFT) underlying large-N pure YM, that
computes sums of the scalar and of the pseudoscalar correlators satisfying the
asymptotic theorem and that implies for the large-N joint scalar and
pseudoscalar glueball spectrum exact linearity in the masses squared. On the
infrared side we test the prediction of the exact linearity in the TFT by
Meyer-Teper lattice numerical computation of the masses of the low-lying
glueballs in SU(8) YM, finding accurate agreement. Besides, we employ the
aforementioned ultraviolet and infrared constraints in order to compare
critically the scalar or pseudoscalar glueball propagators computed in the
framework of the AdS String/large-N Gauge Theory correspondence with those of
the TFT underlying large-N YM. We find that only the TFT satisfies the
ultraviolet and infrared constraints.
