When the center matters: color screening and gluelumps in dihedral lattice gauge theories

TL;DR

This paper demonstrates how confinement phenomena and string breaking in simplified dihedral lattice gauge theories are driven by the center structure, revealing insights into QCD-like physics through numerical and theoretical analysis.

Contribution

It shows the role of the center subgroup in confinement and string breaking in dihedral lattice gauge theories, connecting these phenomena to simpler models of QCD.

Findings

Confinement is linked to the presence of a $bZ_2$ center subgroup.

String breaking can occur via electric field fluctuations without particle-antiparticle pairs.

Finite-range interactions between gluelumps are suggested in the continuum limit.

Abstract

Confinement is one of the hallmarks of quantum chromodynamics (QCD). Yet, its first-principle characterization, even in simpler models, remains elusive. Through a combination of group-theoretical arguments and numerical analysis, we show that the physical consequences of confinement in a class of discrete non-Abelian lattice gauge theories (LGTs), the dihedral groups $D_N$, are intimately connected with the presence of a $\mathbb{Z}_2$ central subgroup. When the center is trivial (for odd $N$), static charges are screened by a gluon cloud, forming composite objects known in SU$(N)$ gauge theories as gluelumps. This finding implies that string breaking can occur through fluctuations of the electric field only, without the need to nucleate particle--antiparticle pairs from the vacuum. Furthermore, numerical analysis hints at finite-range interactions between the gluelumps in the continuum limit. Our results showcase how the rich and intricate physics typically associated with QCD can emerge in much simpler discrete non-Abelian LGTs, making them ideal settings to test this phenomenology both in numerical calculations and in near-term quantum devices.