The Analysis of Space-Time Structure in QCD Vacuum I: Localization vs Global Behavior in Local Observables and Dirac Eigenmodes

Abstract

The structure of QCD vacuum can be studied from first principles using lattice-regularized theory. This line of research entered a qualitatively new phase recently, wherein the space-time structure (at least for some quantities) can be directly observed in configurations dominating the QCD path integral, i.e. without any subjective processing of typical configurations. This approach to QCD vacuum structure does not rely on any proposed picture of QCD vacuum but rather attempts to characterize this structure in a model-independent manner, so that a coherent physical picture of the vacuum can emerge when such unbiased numerical information accumulates to a sufficient degree. An important part of this program is to develop a set of suitable quantitative characteristics describing the space-time structure in a meaningful and physically relevant manner. One of the basic pertinent issues here is whether QCD vacuum dynamics can be understood in terms of localized vacuum objects, or whether such objects behave as inherently global entities. The first direct studies of vacuum structure strongly support the latter. In this paper, we develop a formal framework which allows to answer this question in a quantitative manner. We discuss in detail how to apply this approach to Dirac eigenmodes and to basic scalar and pseudoscalar composites of gauge fields (action density and topological charge density). The approach is illustrated numerically on overlap Dirac zeromodes and near-zeromodes. This illustrative data provides direct quantitative evidence supporting our earlier arguments for the global nature of QCD Dirac eigenmodes.

20 pages, 5 figures; v2: reference added and typos corrected; v3: minor modifications, version to appear in Nuclear Physics B; v4: erratum: Eq. (6) fixed

References in corpus (8)

• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• Localization in Lattice QCD
• Fine tuned vortices in lattice SU(2) gluodynamics
• Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
• Chiral Logs in Quenched QCD
• Topological lumps and Dirac zero modes in SU(3) lattice gauge theory on the torus
• Low-dimensional long-range topological structure in the QCD vacuum
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Cited by in corpus (13)

• Inherently Global Nature of Topological Charge Fluctuations in QCD
• Calorons and dyons at the thermal phase transition analyzed by overlap fermions
• Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum
• Laplacian modes probing gauge fields
• Chiral Symmetry Breaking on the Lattice
• Coherent Topological Charge Structure in $C{P}^{N-1}$ Models and QCD
• Chiral superfluidity of the quark-gluon plasma
• Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite Temperature
• Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics
• Adjoint modes as probes of gauge field structure
• Confining string and its widening in HP1 embedding approach
• The Analysis of Space-Time Structure in QCD Vacuum II: Dynamics of Polarization and Absolute X-Distribution
• On the Continuum Limit of Topological Charge Density Distribution