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 the latticeregularized 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 zero modes and near-zero modes. This illustrative data provides direct quantitative evidence supporting our earlier arguments for the global nature of QCD Dirac eigenmodes.

Laplacian modes probing gauge fields

“…At this point it is desirable to discuss more quantitatively the feature of localization of the Laplacian modes. We have found it useful to add to the IPR measurements done so far a description suggested by Horvath [39]. It compares how quickly clusters (in our case of large modulus of the Laplacian mode) grow in size and how much -at the same time -they gain in norm, when their total volume increases by lowering the lower cutoff in the cluster definition.…”

Chiral superfluidity of the quark–gluon plasma

“…In Refs. [22][23][24][25][26][27] it has been discovered and confirmed by [28,29] that topological charge density forms long-range coherent global structures around a locally one-dimensional network of strong fields (so-called "skeleton"). Though the simulations were performed for low temperatures, the skeletons could very well survive slightly above the deconfinement transition, since there is a corresponding long-range order of gluonic fields [30] in the case of nonvanishing topological susceptibility.…”

Center Vortices and Topological Charge

“…al [61][62][63][64][65] and agrees well with a vortex picture of χSB. Since the QCD-vacuum is strongly non-perturbative, it does not contain semiclassical instantons [66,67] but is crowded with topologically charged objects which, after smooth reduction of the action (also known as cooling), may become instantons. In pure SU (3) lattice gauge theory in a typical equilibrium configuration about 80% of space-time points are covered by two oppositely-charged connected structures built of elementary three-dimensional coherent hypercubes.…”