Inherently Global Nature of Topological Charge Fluctuations in QCD

TL;DR

This paper demonstrates that topological charge fluctuations in QCD are inherently global, forming extended structures rather than localized concentrations, which challenges traditional localized models and suggests a global brane-like description.

Contribution

It provides numerical evidence that topological fluctuations in QCD are globally organized, not localized, and that susceptibility saturation occurs only after global structures are formed.

Findings

Topological susceptibility saturates after global structures form.

Localized regions account for less than 4% of space-time at susceptibility saturation.

Topological charge fluctuations are inherently global, not localized.

Abstract

We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is low-dimensional and geometrically global, i.e. consisting of connected sign-coherent regions with local dimensions 1<= d < 4, and spreading over arbitrarily large space--time distances. Here we show that the space-time structure that is responsible for the origin of topological susceptibility indeed exhibits global behavior. In particular, we show numerically that topological fluctuations are not saturated by localized concentrations of most intense topological charge density. To the contrary, the susceptibility saturates only after the space-time regions with most intense fields are included, such that geometrically global structure is already formed. We demonstrate this result both at the fundamental level (full topological density) and at low energy (effective density). The drastic mismatch between the point of fluctuation saturation (~ 50% of space-time at low energy) and that of global structure formation (<4% of space-time at low energy) indicates that the ordered space-time structure in topological charge is inherently global and that topological charge fluctuations in QCD cannot be understood in terms of individual localized pieces. Description in terms of global brane-like objects should be sought instead.