Laplacian modes probing gauge fields

TL;DR

This paper demonstrates that low-lying Laplacian eigenmodes effectively reveal properties of SU(2) gauge fields, including monopole localization and confining structures, using a novel Fourier-like filtering method.

Contribution

It introduces a new low-pass filter based on Laplacian eigenmodes that preserves confinement and classical structures in lattice gauge configurations.

Findings

Laplacian modes localize monopoles in calorons

Phase boundary conditions affect mode localization

The filter reproduces classical structures and preserves confinement

Abstract

We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.