Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics

TL;DR

This paper investigates how cooling affects the spatial distribution of topological charge in SU(2) lattice gauge theory, revealing a transition in the fractal dimension of localized regions from 2-3 towards the full space dimension, indicating a loss of topological features.

Contribution

It demonstrates how cooling alters the topological charge distribution's fractal properties in SU(2) lattice gluodynamics, highlighting the destruction of key topological features.

Findings

Cooling increases the Hausdorff dimension of topological charge regions.

Topological charge distribution becomes more uniform with cooling.

Essential properties of the topological charge are lost during cooling.

Abstract

We study the effect of cooling on the spatial distribution of the topological charge density in quenched SU(2) lattice gauge theory with overlap fermions. We show that as the gauge field configurations are cooled, the Hausdorff dimension of regions where the topological charge is localized gradually changes from d = 2..3 towards the total space dimension. Therefore, the cooling procedure destroys some of the essential properties of the topological charge distribution.