Realization of chiral symmetry in the domain model of QCD

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The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks, a strong correlation of the local chirality of quark modes, and a duality of the background domainlike gluon field. Quark fluctuations satisfy a chirality violating boundary condition parametrized by a random chiral angle ${\ensuremath{\alpha}}_{j}$ on the jth domain. The free energy of an ensemble of $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ domains depends on ${{\ensuremath{\alpha}}_{j},j=1,\dots{},N}$ through the logarithm of the quark determinant. Its parity odd part is given by the axial anomaly. The anomaly contribution to the free energy suppresses continuous axial $U(1)$ degeneracy in the ground state, leaving only a residual axial $Z(2)$ symmetry. This discrete symmetry and the flavor ${SU(N}_{f}{)}_{L}\ifmmode\times\else\texttimes\fi{}{SU(N}_{f}{)}_{R}$ chiral symmetry in turn are spontaneously broken with a quark condensate arising due to the asymmetry of the spectrum of the Dirac operator. In order to illustrate the splitting between the ${\ensuremath{\eta}}^{\ensuremath{'}}$ from octet pseudoscalar mesons realized in the domain model, we estimate the masses of the light pseudoscalar and vector mesons.