On the Local Structure of Topological Charge Fluctuations in QCD

TL;DR

This paper introduces an eigenmode expansion of the lattice topological charge density to analyze QCD fluctuations, revealing that topological charge does not mainly form quantized lumps, challenging previous assumptions about chiral symmetry breaking mechanisms.

Contribution

It proposes a new eigenmode-based framework for studying topological charge fluctuations in QCD, offering insights into the non-lump nature of topological charge distributions.

Findings

Topological charge in QCD does not predominantly appear as quantized lumps.

The effective density describes smooth space-time charge distributions relevant for light fermions.

Charge fluctuations in spherical regions have a continuous distribution ending around 0.5.

Abstract

We consider the lattice topological charge density introduced by Hasenfratz, Laliena and Niedermayer and propose its eigenmode expansion as a tool to investigate the structure of topological charge fluctuations in QCD. The resulting effective density is built from local chiralities studied previously. At every order of the expansion the density exactly sums up to the global topological charge, and the leading term describes the maximally smooth space-time distribution of charge relevant for propagating light fermions. We use this framework to demonstrate our previous suggestion that the bulk of topological charge in QCD does not effectively appear in the form of quantized unit lumps. Our conclusion implies that it is unlikely that the mixing of "would-be" zeromodes associated with such lumps is the prevalent microscopic mechanism for spontaneous chiral symmetry breaking in QCD. We also present first results quantitatively characterizing the space-time behavior of effective densities. For coherent fluctuations contained in spherical regions we find a continuous distribution of associated charges essentially ending at ~0.5.