Uncovering Low-Dimensional Topological Structure in the QCD Vacuum

TL;DR

This paper reveals a low-dimensional topological order in the QCD vacuum, showing that about 80% of space-time is covered by interconnected 3D hypercubes with opposite charges, indicating a structured coherence.

Contribution

It demonstrates the presence of a low-dimensional topological structure in the QCD vacuum using Ginsparg-Wilson fermions, extending previous findings on sign coherence.

Findings

Approximately 80% of space-time points are covered by two oppositely charged structures.

Structures are built of 3D hypercubes connected through 2D faces.

Chiral smoothing is essential for observing this topological coherence.

Abstract

Recently, we have pointed out that sign-coherent 4-dimensional structures can not dominate topological charge fluctuations in QCD vacuum at all scales. Here we show that an enhanced lower-dimensional coherence is possible. In pure SU(3) lattice gauge theory we find that in a typical equilibrium configuration about 80% of space-time points are covered by two oppositely-charged connected structures built of elementary 3-dimensional coherent hypercubes. The hypercubes within the structure are connected through 2-dimensional common faces. We suggest that this coherence is a manifestation of a low-dimensional order present in the QCD vacuum. The use of a topological charge density associated with Ginsparg-Wilson fermions ("chiral smoothing") is crucial for observing this structure.