Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum

TL;DR

This paper provides evidence for low-dimensional, long-range topological charge structures in the QCD vacuum, revealing sheets and a skeleton that could influence chiral symmetry breaking.

Contribution

It introduces the discovery of extended, low-dimensional topological structures in the QCD vacuum using lattice gauge theory, highlighting their potential physical significance.

Findings

Dominance of two oppositely-charged sheets covering 80% of space-time

Sheets are built from connected 3D cubes forming curved manifolds or fractals

A 1D skeleton within the sheets may be relevant for chiral symmetry breaking

Abstract

While sign-coherent 4-dimensional structures cannot dominate topological charge fluctuations in the QCD vacuum at all scales due to reflection positivity, it is possible that enhanced coherence exists over extended space-time regions of lower dimension. Using the overlap Dirac operator to calculate topological charge density, we present evidence for such structure in pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium configuration is dominated by two oppositely-charged sign-coherent connected structures (``sheets'') covering about 80% of space-time. Each sheet is built from elementary 3-d cubes connected through 2-d faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18% of the most intense space-time points organized into a global long-range structure, involving connected parts spreading over maximal possible distances. We find that the skeleton is locally 1-dimensional and propose that its geometrical properties might be relevant for understanding the possible role of topological charge fluctuations in the physics of chiral symmetry breaking.