Confinement, chiral symmetry breaking, and the axial anomaly from domain formation at intermediate resolution - art. no. 085001

Based on general renormalization group arguments, Polyakov's loop-space for malism, and recent analytical lattice arguments. suggesting, after Abelian gauge fixing, a description of pure gluodynamics by means of a Georgi-Glash ow like model, the corresponding vacuum fields are defined in a nonlocal wa y. Using lattice information on the gauge invariant field strength correlat or in full QCD, the resolution scale Lambda (b) at which these fields becom e relevant in the vacuum. is determined. For SU(3) gauge theory it is found that Lambda (b)similar to2.4 GeV, 3.1 GeV, and 4.2 GeV for (N-F = 4, m(q) = 18 MeV), (N-F = 4, m(q) = 36 MeV), and pure gluodynamics, repectively. Im plications for the operator product expansion of physical correlators are d iscussed. It is argued that the emergence of magnetic (anti)monopoles in th e vacuum at resolution Lambda (b) is a direct consequence of the randomness in the formation of a low entropy Higgs condensate. This implies a breakin g of chiral symmetry and a proliferation of the axial UM anomaly at this sc ale already. Justifying Abelian projection, a decoupling of non-Abelian gau ge field fluctuations from the dynamics occurs. The condensation of (anti)m onopoles at Lambda (c)<<Lambda>(b) follows from the demand that vacuum fiel ds ought to have vanishing action at any resolution. As monopoles condense they are reduced to their cores, and hence they become massless. Apparently broken gauge symmetries at resolutions Lambda (c)<<Lambda>less than or equ al to Lambda (b), are restored in this process.