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Glueball and meson propagators of any spin in large-N QCD

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.