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Based on general renormalization group arguments, Polyakov's loop-spaceformalism, and recent analytical lattice arguments, suggesting, after Abeliangauge fixing, a description of pure gluodynamics by means of a Georgi-Glashowlike model, the corresponding vacuum fields are defined in a non-local way.Using lattice information on the gauge invariant field strength correlator infull QCD, the resolution scale $\La_b$, at which these fields become relevantin the vacuum, is determined. For SU(3) gauge theory it is found that$\La_b\sim$ 2.4 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. Implications for the operatorproduct expansion of physical correlators are discussed. It is argued that theemergence of magnetic (anti)monopoles in the vacuum at resolution $\La_b$ is adirect consequence of the randomness in the formation of a low entropy Higgscondensate. This implies a breaking of chiral symmetry and a proliferation ofthe axial U(1) anomaly at this scale already. Justifying Abelian projection, adecoupling of non-Abelian gauge field fluctuations from the dynamics occurs.The condensation of (anti)monopoles at $\La_c<\La_b$ follows from the demandthat vacuum fields ought to have vanishing action at any resolution. Asmonopoles condense they are reduced to their cores, and hence they becomemassless. Apparently broken gauge symmetries at resolutions $\La_c<\La\le\La_b$are restored in this process.Comment: 11 pages, 3 figure

Confinement, chiral symmetry breaking, and the axial anomaly from domain formation at intermediate resolution