The Casimir Effect in (3+1)-dimensional lattice Yang-Mills theory at finite temperature: the unexpected universality of quarkiton and glueton boundary states

TL;DR

The paper studies Casimir boundary effects in (3+1)-D SU(3) Yang-Mills theory using lattice simulations with a chromometallic mirror at finite temperature near $T \approx 0.78\,T_c$. The heavy-quark free energy near the mirror is renormalized and fitted to a Cornell form, revealing a linear confining term and a boundary-state string tension $\sigma_Q$, with $\mathcal{R}_{Q|} = \mathcal{R}_{g|} \approx 0.294$. The comparison with the gluon boundary state (glueton) yields a matching universal ratio to the bulk mass gap, $\mathcal{R} \approx 0.293$, suggesting a universal scaling of boundary-state properties across quark and gluon sectors. These results support the physical relevance of quarkitons and gluetons as boundary excitations and imply a broader role for edge modes and domain-wall mirrors in non-Abelian gauge theories.

Abstract

In our earlier work on the Casimir effect in (3+1)-dimensional Yang-Mills theory, we identified two novel nonperturbative states arising in QCD with boundaries: the glueton and the quarkiton. The glueton, or "gluon exciton", is a colorless bound state formed by gluons interacting with their negatively colored images in a chromometallic mirror. The quarkiton, or "quark exciton", is a meson-like state comprising a heavy quark attracted to its image through the mirror. In this study, we extend our analysis to finite temperatures near the deconfinement phase transition $(T \approx 0.78 T_c)$, where we observe a linear potential between a color-neutral chromometallic mirror and a heavy test quark. Our result suggests that the quarkiton state can have a physical relevance since mirrors for photons and, presumably, gluons can be realized in field theories as domain-wall solutions. Furthermore, we find a striking universality: the ratio of the glueton mass to the bulk $0^{++}$ glueball mass - defining the bulk mass gap - matches the ratio of the quarkiton string tension to the string tension between quark and anti-quark in the absence of the mirror, with a value $\mathcal{R} = 0.294(11)$.

Figures (2)

• Figure 1: Unrenormalized free energy of heavy quark as a function of distance to the mirror in physical units at a fixed temperature.
• Figure 2: The renormalized free energy of heavy quark as a function of distance to the mirror in the physical units at the fixed temperature $T = 0.78 T_c$. The fit by the Cornell potential \ref{['eq_cornell_fit']} is shown by the solid curve.