Low-dimensional long-range topological structure in the QCD vacuum

Lattice topological charge associated with Ginsparg-Wilson fermions exhibits generic topological stability over quantum ensemble of configurations contributing to the QCD path integral. Moreover, the underlying chiral symmetry leads to the suppression of ultraviolet noise in the associated topological charge densities ("chiral smoothing"). This provides a solid foundation for the direct study of the role of topological charge fluctuations in the physics of QCD vacuum. Using these tools it was recently demonstrated that: (a) there is a well-defined space-time structure (order) in topological charge density (defined through overlap fermions) for typical configurations contributing to QCD path integral; (b) this fundamental structure is low-dimensional, exhibiting sign-coherent behavior on subsets of dimension less than four and not less than one; (c) the structure has a long-range global character (spreading over maximal space-time distances) and is built around the locally one-dimensional network of strong fields (skeleton). In this talk we elaborate on certain aspects and implications of these results.