Laplacian modes as a filter

TL;DR

This paper explores the use of low-lying Laplacian eigenmodes as a novel filtering technique for lattice gauge configurations, revealing classical structures and preserving confinement with minimal modes.

Contribution

It introduces a new Laplacian mode-based filter for lattice gauge fields that captures classical features and maintains the confining potential with few modes.

Findings

Laplacian modes localize monopole constituents in calorons

The lowest mode hops with boundary condition changes

The filter preserves the confining potential with few modes

Abstract

We compute low-lying eigenmodes of the gauge covariant Laplace operator on the lattice at finite temperature. For classical configurations we show how the lowest mode localizes the monopole constituents inside calorons and that it hops upon changing the boundary conditions. The latter effect we observe for thermalized backgrounds, too, analogously to what is known for fermion zero modes. We propose a new filter for equilibrium configurations which provides link variables as a truncated sum involving the Laplacian modes. This method not only reproduces classical structures, but also preserves the confining potential, even when only a few modes are used.