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Title: Topological Charge and the Laminar Structure of the QCD Vacuum

Abstract

Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, coherent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. In this talk I discuss the interpretation of these Monte Carlo results in terms of our current theoretical understanding of theta-dependence and topological structure in asymptotically free gauge theories.

Authors:
 [1]
  1. University of Virginia, Charlottesville, VA 22904 (United States)
Publication Date:
OSTI Identifier:
21056814
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 892; Journal Issue: 1; Conference: QCHS7: 7. conference on quark confinement and the hadron spectrum, Ponta Delgada, Acores (Portugal), 2-7 Sep 2006; Other Information: DOI: 10.1063/1.2714378; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; FIELD OPERATORS; FOUR-DIMENSIONAL CALCULATIONS; GAUGE INVARIANCE; MONTE CARLO METHOD; QUANTUM CHROMODYNAMICS; SU-3 GROUPS; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY; VACUUM STATES

Citation Formats

Thacker, H. B.. Topological Charge and the Laminar Structure of the QCD Vacuum. United States: N. p., 2007. Web. doi:10.1063/1.2714378.
Thacker, H. B.. Topological Charge and the Laminar Structure of the QCD Vacuum. United States. doi:10.1063/1.2714378.
Thacker, H. B.. Tue . "Topological Charge and the Laminar Structure of the QCD Vacuum". United States. doi:10.1063/1.2714378.
@article{osti_21056814,
title = {Topological Charge and the Laminar Structure of the QCD Vacuum},
author = {Thacker, H. B.},
abstractNote = {Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, coherent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. In this talk I discuss the interpretation of these Monte Carlo results in terms of our current theoretical understanding of theta-dependence and topological structure in asymptotically free gauge theories.},
doi = {10.1063/1.2714378},
journal = {AIP Conference Proceedings},
number = 1,
volume = 892,
place = {United States},
year = {Tue Feb 27 00:00:00 EST 2007},
month = {Tue Feb 27 00:00:00 EST 2007}
}
  • 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 fractalmore » 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.« less
  • APE smearing and overlap-Dirac operator are combined to filter QCD vacuum configurations. The results obtained from overlap fermions and improved 5Li cooling are compared, both of them exhibit structures of dilute liquid of instanton. Finally the overlap fermions, improved 5Li cooling and APE smearing are combined to calculate the topological charge and identify the structure of QCD vacuum. The results suggest dilute liquid of instanton dominance of topological charge fluctuations in quenched lattice QCD.
  • Long-range order of a specific kind has recently been found directly in configurations dominating the regularized QCD path integral. In particular, a low-dimensional global structure was identified in typical space-time distributions of topological charge defined via the overlap Dirac matrix. The presence of the order has been concluded from the fact that the structure disappears after random permutation of position coordinates in measured densities. Here we complete the argument for the reality of this structure (namely the conjecture that its existence is a consequence of QCD dynamics and not an artifact of the overlap-based definition of lattice topological field) bymore » showing that the structure ceases to exist after randomizing the space-time coordinates of the underlying gauge field. This implies that the long-range order present in the overlap-based topological density is indeed a manifestation of the QCD vacuum, and that the notion of the fundamental structure (structure involving relevant features at all scales) is viable.« less
  • We consider the lattice topological charge density introduced by Hasenfratz, Laliena, and Niedermayer and propose its eigenmode expansion as a tool to investigate the structure of topological charge fluctuations in QCD. The resulting effective density is built from local chiralities studied previously. At every order of the expansion, the density exactly sums up to the global topological charge, and the leading term describes the maximally smooth space-time distribution of charge relevant for propagating light fermions. We use this framework to demonstrate our previous suggestion that the bulk of the topological charge in QCD does not effectively appear in the formmore » of quantized unit lumps. Our conclusion implies that it is unlikely that the mixing of -would-be- zero modes associated with such lumps is the prevalent microscopic mechanism for spontaneous chiral symmetry breaking in QCD. We also present the first results quantitatively characterizing the space-time behavior of effective densities. For coherent fluctuations contained in spherical regions, we find a continuous distribution of associated charges essentially ending at [approximate] 0.5.« less
  • In an effort to clarify the significance of the recent observation of long-range topological charge coherence in QCD gauge configurations, we study the local topological charge distributions in two-dimensional CP{sup N-1} sigma models, using the overlap Dirac operator to construct the lattice topological charge. We find long-range sign coherence of topological charge along extended one-dimensional structures in two-dimensional spacetime. We discuss the connection between the long-range topological structure found in CP{sup N-1} and the observed sign coherence along three-dimensional sheets in four-dimensional QCD gauge configurations. In both cases, coherent regions of topological charge form along membranelike surfaces of codimension one.more » We show that the Monte Carlo results, for both two-dimensional and four-dimensional gauge theory, support a view of topological charge fluctuations suggested by Luescher and Witten. In this framework, the observed membranes are associated with boundaries between ''k-vacua,'' characterized by an effective local value of {theta} which jumps by {+-}2{pi} across the boundary.« less