The local structure of topological charge fluctuations in QCD

TL;DR

This paper introduces a new method using Dirac eigenmode filtering to analyze topological charge fluctuations in QCD, revealing that topological charge does not mainly form quantized lumps and providing insights into chiral symmetry breaking mechanisms.

Contribution

The study applies Dirac eigenmode filtering with Ginsparg-Wilson fermions to investigate the local structure of topological charge in QCD, challenging the lump-based picture of topological charge.

Findings

Topological charge in QCD is not primarily composed of quantized lumps.

The distribution of charges in coherent regions ends around 0.5.

Overlap-operator correlators show non-positivity at nonzero distances, confirming operator locality.

Abstract

We introduce the Dirac eigenmode filtering of topological charge density associated with Ginsparg-Wilson fermions as a tool to investigate the local structure of topological charge fluctuations in QCD. The resulting framework is used to demonstrate that the bulk of topological charge in QCD does not appear in the form of unit quantized lumps. This means that the mixing of "would-be" zeromodes associated with such lumps is probably not the prevalent microscopic mechanism for spontaneous chiral symmetry breaking in QCD. To characterize the coherent local behavior in topological charge density at low energy, we compute the charges contained in maximal coherent spheres enclosing non-overlapping peaks. We find a continuous distribution essentially ending at ~0.5. Finally, we study, for the first time, the overlap-operator topological-charge-density correlators and find consistency with non-positivity at nonzero physical distance. This represents a non-trivial check on the locality (in gauge paths) of the overlap Dirac operator for realistic gauge backgrounds.