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

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.