On the chirality of quark modes

A model for the QCD vacuum based on a domainlike structured background gluon field with definite duality attributed to the domains has been shown elsewhere to give confinement of static quarks, a reasonable value for the topological susceptibility and indications that chiral symmetry is spontaneously broken. In this paper we study in detail the eigenvalue problem for the Dirac operator in such a gluon mean field. A study of the local chirality parameter shows that the lowest nonzero eigenmodes possess a definite mean chirality correlated with the duality of a given domain. A probability distribution of the local chirality qualitatively reproduces histograms seen in lattice simulations.