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

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.