Cluster duality

Abstract

It is well known that the linear mass spectrum of light mesons in the large- N c limit is dual to the perturbative QCD continuum. We find the form of the linear spectrum which is maximally dual to the perturbation theory. The obtained ansatz turns out to be the spectrum of the Lovelace–Shapiro dual amplitude. This spectrum is chirally symmetric in the sense that it corresponds to zero values for the order parameters of chiral symmetry breaking in QCD. We further assume that the actual spectrum is dual to the maximally dual one within the QCD sum rules based on OPE and in this way recover some known important relations and statements. The experimental spectrum seems to support the assumed duality: The masses of resonances cluster near certain equidistant values of energy squared and the positions of clustering follow the maximally dual ansatz. The latter fact signals the chiral symmetry restoration in the excited states. We discuss also two topics of recent interest: nonlinear corrections to the string-like spectrum and the dimension-two gluon condensate.