Towards an Abelian Formulation of Lattice QCD Confinement

TL;DR

This paper investigates the spectral properties of abelian-projected QCD in pure gauge SU(3), revealing dominant resonance behavior and evidence of confinement through spectral density analysis of plaquettes.

Contribution

It introduces a spectral density approach to analyze abelian-projected QCD operators, providing new insights into confinement mechanisms in lattice gauge theory.

Findings

APQCD dominated by a q=L=1 resonance

Evidence for weakly coupled L=2 plaquettes

APQCD exhibits confinement despite higher beta values

Abstract

We probe for operators occurring in the APQCD(``abelian-projected QCD'') action by evaluating abelian-projected $1$-plaquette spectral densities in pure gauge $SU(3)$ fixed to maximal abelian gauge. Couplings $B_{APQCD}(q,L)$ are extracted from the spectral densities for each representation $q$, $L\times L$ plaquette. While APQCD is dominated by a $q=L=1$ resonance, we also find evidence for weakly coupled $L=2$ plaquettes. Moreover, since $B_{APQCD}(1,1) > B_{QED}(1,1)$ even if $\beta_{QED} > \beta_c$, $L>1$ plaquettes must be significant since APQCD is confining.