Deconfinement on ${\mathbb{Z}}_F$ and Axion Domain Walls

We investigate the nontrivial dynamics on ${\mathbb{Z}}_F$ domain walls and compute their tension in quantum chromodynamics (QCD) compactified on a circle with $N$ colors and $F<N$ massless fundamental flavors. In the process, we obtain insights on the ${\eta }^{\mathrm{\prime }}$ meson’s potential in a regime where it is heavy and comparable in mass to other QCD resonances, as in Nature. We employ a center-stabilized compactification of QCD on a small circle of size $L$ with color-flavor twisted boundary conditions for the quarks. We demonstrate that probe particles in color representations of $N$-ality $N\mathrm{/}\mathrm{g}\mathrm{c}\mathrm{d}(N,F)$ are deconfined on the ${\mathbb{Z}}_F$ domain walls whenever $N$ and $F$ are not coprime. This is reminiscent of deconfinement on axion domain walls in pure Yang–Mills. Finally, in the double scaling limit $N\to \mathrm{\infty }$ keeping $NL$ and $F$ fixed, the infrared spectrum spans an emergent dimension. We establish that the ${\mathbb{Z}}_F$ domain walls are dual to electrostatic charge distributions in this emergent dimension. This duality allows us to compute their tension analytically and find a different tension scaling at large-$N$ between ${\mathbb{Z}}_F$ domain walls in QCD and axion domain walls in pure Yang–Mills, in center-stabilized compactifications.