TY - JOUR

T1 - Low-dimensional long-range topological charge structure in the QCD vacuum

AU - Horváth, I.

AU - Dong, S. J.

AU - Draper, T.

AU - Lee, F. X.

AU - Liu, K. F.

AU - Mathur, N.

AU - Thacker, H. B.

AU - Zhang, J. B.

PY - 2003

Y1 - 2003

N2 - 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 3D cubes connected through 2D faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4D 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.

AB - 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 3D cubes connected through 2D faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4D 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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U2 - 10.1103/PhysRevD.68.114505

DO - 10.1103/PhysRevD.68.114505

M3 - Article

AN - SCOPUS:1642454521

SN - 1550-7998

VL - 68

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 11

ER -