Qualitative solution of QCD sum rules

Abstract

We show how such important features of QCD as chiral symmetry breaking or the formation of a mass-gap can be directly traced from QCD sum rules for two point functions assuming, in the large number of colors limit, exact duality between the operator product expansion and the spectrum described by linearly (or nearly linear) rising Regge trajectories as predicted by string theory. We see how the presence of chiral symmetry breaking is intimately related to confinement in this scenario, as expected from general arguments, and how Regge trajectories change when chiral symmetry is broken. As a result the whole meson mass spectrum can be parametrized with a good accuracy by the constant $f_{\pi}$ only, thus realizing the program proposed by Migdal some time ago.