Vacuum structure and the axion walls in gluodynamics and QCD with light quarks

Large $N_c$ pure gluodynamics was shown to have a set of metastable vacua with the gluonic domain walls interpolating between them. The walls may separate the genuine vacuum from an excited one or two excited vacua which are unstable at finite $N_c.$ One may attempt to stabilize them by switching on the axion field. We study how the light quarks and the axion affect the structure of the domain walls. In pure gluodynamics (with the axion field) the axion walls acquire a very hard gluonic core. Thus, we deal with a wall “sandwich” which is stable at finite $N_c.$ In the case of the minimal axion, the wall “sandwich” is in fact a $“2\pi ”$ wall; i.e., the corresponding field configuration interpolates between identical hadronic vacua. The same properties hold in QCD with three light quarks and very large $N_c.$ However, in the realistic case of three-color QCD the phase corresponding to the axion field profile in the axion wall is screened by a dynamical phase associated with the ${\eta }^{\prime },$ so that the gluon component of the wall is not excited. We propose a toy Lagrangian which models these properties and allows one to get exact solutions for the domain walls.