Perfect Abelian dominance of confinement in quark-antiquark potential in SU(3) lattice QCD

TL;DR

This study demonstrates that in SU(3) lattice QCD, the Abelian component of the quark-antiquark potential accounts for nearly all of the confinement, supporting the Abelian dominance hypothesis in the dual superconductor model.

Contribution

It provides numerical evidence of perfect Abelian dominance in quark confinement within SU(3) lattice QCD, highlighting the significance of Abelian projection in understanding confinement.

Findings

Almost perfect Abelian dominance for string tension.

Nontrivial summation relation of potentials.

Confirmation of Abelian dominance in SU(3) lattice QCD.

Abstract

In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with $32^4$ at $\beta$=6.4 (i.e., $a \simeq$ 0.058 fm). We investigate the static quark-antiquark potential $V(r)$, its Abelian part $V_{\rm Abel}(r)$ and its off-diagonal part $V_{\rm off}(r)$, respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., $\sigma_{\rm Abel} \simeq \sigma$ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of $V(r) \simeq V_{\rm Abel}(r) + V_{\rm off}(r)$.