Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum

Details Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum

2003-02-18

arxiv.org/abs/hep-lat/0302009v2

Phys.Rev.D68:114505,2003

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations provided, figure and references added, published version

Scientific paper

10.1103/PhysRevD.68.114505

While sign-coherent 4-dimensional structures cannot dominate topological charge fluctuations in the QCD vacuum at all scales due to reflection positivity, it is possible that enhanced coherence exists over extended space-time regions of lower dimension. Using the overlap Dirac operator to calculate topological charge density, we present evidence for such structure in pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium configuration is dominated by two oppositely-charged sign-coherent connected structures (``sheets'') covering about 80% of space-time. Each sheet is built from elementary 3-d cubes connected through 2-d faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18% of the most intense space-time points organized into a global long-range structure, involving connected parts spreading over maximal possible distances. We find that the skeleton is locally 1-dimensional and propose that its geometrical properties might be relevant for understanding the possible role of topological charge fluctuations in the physics of chiral symmetry breaking.

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