QCD Dirac spectrum and components of the gauge field

TL;DR

This paper investigates how different components of the gauge field in SU(3) lattice QCD influence the Dirac spectrum, revealing the significance of momentum components and SU(2) subgroups in shaping low-lying eigenvalues and topological features.

Contribution

It provides a detailed analysis of the relationship between gauge field components and the Dirac spectrum, highlighting the roles of momentum and subgroup structures in lattice QCD.

Findings

Broad momentum components are relevant for low-lying Dirac eigenvalues and topological charges.

SU(2) subgroup components mimic SU(2) gauge field behavior in the Dirac spectrum.

Connection with chiral random matrix theory is discussed.

Abstract

We analyze the relation between the Dirac spectrum and the gauge field in SU(3) lattice QCD. We focus on how components of the gauge field are related to the Dirac spectrum. First, we consider momentum components of the gauge field. It turns out that the broad region of momentum components is relevant for the low-lying Dirac spectrum and zero modes, i.e., topological charges. The connection with chiral random matrix theory is also discussed. Second, we consider an SU(2) subgroup component of the SU(3) gauge field. The SU(2) subgroup component behaves like the SU(2) gauge field in the low-lying Dirac spectrum.