Quantitative comparison of filtering methods in lattice QCD

TL;DR

This paper systematically compares various filtering methods in lattice QCD to reliably identify topological structures, demonstrating their consistency and revealing insights into the QCD vacuum's infrared properties.

Contribution

It provides a comprehensive comparison of filtering techniques in lattice QCD, clarifying ambiguities and confirming the robustness of identified topological structures.

Findings

Different filtering methods yield similar topological structures when used carefully.

Filtered topological charge clusters follow a power-law distribution.

Common structures are free of ambiguities and represent true infrared degrees of freedom.

Abstract

We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice Dirac and Laplace operators. Each of these techniques introduces ambiguities, which can invalidate the interpretation of the results. We show, however, that all these methods, when handled with care, reveal very similar topological structures. Hence, these common structures are free of ambiguities and faithfully represent infrared degrees of freedom in the QCD vacuum. As an application we discuss an interesting power-law for the clusters of filtered topological charge.