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

TL;DR

This paper introduces a model-independent, quantitative framework to analyze the space-time structure of the QCD vacuum, emphasizing the global nature of Dirac eigenmodes through numerical evidence.

Contribution

It develops a formal approach to distinguish localized versus global vacuum structures in QCD, applied to Dirac eigenmodes and gauge field composites, supported by numerical data.

Findings

Dirac eigenmodes exhibit global behavior in QCD vacuum

The framework quantitatively characterizes space-time structures

Numerical evidence supports the global nature of Dirac modes

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.