Testing the self-duality of topological lumps in SU(3) lattice gauge theory

TL;DR

This paper investigates the self-duality properties of topological lumps in SU(3) lattice gauge theory by analyzing spectral sums of the Dirac operator, revealing that near-zero modes are predominantly (anti) self-dual, with reduced self-duality at high temperatures.

Contribution

The study introduces a simple spectral formula linking the Dirac eigenmodes to the field-strength tensor, providing new insights into the self-duality of topological structures in lattice QCD.

Findings

Near-zero modes are mainly (anti) self-dual.

Higher eigenmodes are less self-dual due to quantum fluctuations.

Self-duality diminishes near the spectral gap edge at high temperatures.

Abstract

We discuss a simple formula which connects the field-strength tensor to a spectral sum over certain quadratic forms of the eigenvectors of the lattice Dirac operator. We analyze these terms for the near zero-modes and find that they give rise to contributions which are essentially either self-dual or anti self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more dominated by quantum fluctuations and are less (anti) self-dual. In the high temperature phase of QCD we find considerably reduced (anti) self-duality for the modes near the edge of the spectral gap.