A Visualization of the SU(2) Vacuum on the Lattice

TL;DR

This paper visualizes the SU(2) gauge field vacuum on the lattice, revealing localized peaks resembling instantons, and analyzes their properties, scaling, and gauge dependence through Fourier filtering and comparison with other theories.

Contribution

Introduces a novel visualization method for SU(2) lattice configurations using Fourier filtering to identify and analyze localized topological peaks.

Findings

Peaks resemble instantons and anti-instantons in gauge configurations.

Peak density scales with the string tension as coupling varies.

Fourier filtering evolution compares with cooling methods and reveals gauge dependence.

Abstract

Configurations of pure SU(2) gauge field theory on the lattice are transformed to Landau gauge. After Fourier transformation, large momentum amplitudes are suppressed (filtered) by a variable amount, and the configurations are transformed back to x-space. Spectacular peaks in electric and magnetic field strengths are found, which share many properties with either almost pointlike instantons in regular gauge or with extended anti-instantons in singular gauge. The environment around those peaks are visualized with respect to the action, to the topological charge density, to the gauge fields and to electric and magnetic field strengths. The density of the peaks is of order 1 / fm**4, and it scales according to the string tension under a variation of the coupling constant. The evolution of the peaks under the amount of Fourier filtering is visualy compared to the evolution under cooling, and the gauge dependence of the peaks is discussed. Advantages and shortcomings of this method are discussed, with emphasis on possible strong distortions of the action and topological charge density, which become gauge dependent. Finally, I compare the character of the SU(2)-configurations to those of noncompact abelian theory.