Glueball and meson spectrum in large-N massless QCD

Abstract

We provide outstanding numerical evidence that in large-N massless QCD the joint spectrum of the masses squared, for fixed integer spin s and unspecified parity and charge conjugation, obeys exactly the following laws: m_k^2 = (k+s/2) Lambda_QCD^2 for s even, m_k^2 = 2(k+s/2) Lambda_QCD^2 for s odd, k = 1,2,... for glueballs, and m_n^2 = 1/2 (n+s/2) Lambda_QCD^2, n = 0,1,... for mesons. One of the striking features of these laws is that they imply that the glueball and meson masses squared form exactly-linear Regge trajectories in the large-N limit of massless QCD, all the way down to the low-lying states: A fact unsuspected so far. The numerical evidence is based on lattice computations by Meyer-Teper in SU(8) YM for glueballs, and by Bali et al. in SU(17) quenched massless QCD for mesons, that we analyze systematically. The aforementioned spectrum for spin-0 glueballs is implied by a Topological Field Theory underlying the large-N limit of YM, whose glueball propagators satisfy as well fundamental universal constraints arising from the asymptotic freedom and the renormalization group. No other presently existing model meets both the infrared spectrum and the ultraviolet constraints. We argue that some features of the aforementioned spectrum of glueballs and mesons of any spin could be explained by the existence of a Topological String Theory dual to the Topological Field Theory.