Localization properties of fermions and bosons

TL;DR

This paper reviews lattice studies of the QCD vacuum, revealing a topological structure characterized by alternating thin layers of opposite topological charge, which is probed through the localization of low-lying Dirac eigenmodes.

Contribution

It provides a comprehensive review of recent lattice investigations into the topological structure of the QCD vacuum using fermion and boson localization properties.

Findings

Vacuum exhibits a 'topological sandwich' structure with alternating layers.

Low-lying Dirac eigenmodes reveal the topological features without gauge field smoothing.

The structure is consistent with direct measurements of topological charge density.

Abstract

The topological structure of the QCD vacuum can be probed by monitoring the spatial localization of the low-lying Dirac eigenmodes. This approach can be pursued on the lattice, and unlike the traditional one requires no smoothing of the gauge field. I review recent lattice studies, attempting to extract a consistent description. What emerges is a picture of the vacuum as a ``topological sandwich'' of alternating, infinitely thin 3d layers of opposite topological charge, as originally seen in direct measurements of the topological charge density.