Chiral symmetry and spectrum of Euclidean Dirac operator

Abstract

After recalling some connections between the Spontaneous Breakdown of Chiral Symmetry (SBChS) and the spectrum of the Dirac operator for Euclidean QCD on a torus, we use this tool to reconsider two related issues : the Zweig rule violation in the scalar channel and the dependence of SBChS order parameters on the number N_f of massless flavours. The latter would result into a great variety of SBChS patterns in the (N_f,N_c) plane, which could be studied through so-called Leutwyler-Smilga sum rules in association with lattice computations of the Dirac spectrum.