studying the properties of domain wall network as QCD vacuum

The general topic of master's work relates to improvement of understanding the mechanisms of confinement in quantum chromodynamics.the approach is based on the specific background vacuum gluon configurations,almost everywhere homogeneous Abelian gluon fields,represented by the ensemble of domain wall networks.the specific task was to investigate the role of quark low-lying modes in the presence of these background fields for stabilization of a finite size of a space-time regions where the background (anti)self-dual Abelian field can be seen as homogeneous.An indication has been obtained that indeed the effective potential of QCD may have a clear minimum at nonzero value of the strength of Abelian self-dual field and finite value of the IR cutoff parameter which models the domain size.the minimum of the effective potential (energy density inside domain) is estimated as$R\approx 1.76/\sqrt{B}\sim .42 {\rm fm},$ which is a qualitatively reasonable value for the optimal domain size, at least by the order of magnitude.