Boundary states and Non-Abelian Casimir effect in lattice Yang-Mills theory

Abstract

Using first-principle numerical simulations, we investigate the Casimir effect in zero-temperature SU(3) lattice gauge theory in 3+1 spacetime dimensions. The Casimir interaction between perfect chromometallic mirrors reveals the presence of a new gluonic state with the mass $m_{\mathrm{gt}} = 1.0(1)\sqrt{\sigma} = 0.49(5)\,\mathrm{GeV} = 0.29(3) M_{0^{++}}$ which is substantially lighter than the $0^{++}$ groundstate glueball. We call this excitation ``glueton'' interpreting it as a non-perturbative colorless state of gluons bound to their negatively colored images in the chromometallic mirror. The glueton is a gluonic counterpart of a surface electron-hole exciton in semiconductors. We also show that a heavy quark is attracted to the neutral chromometallic mirror, thus supporting the existence of a ``quarkiton'' (a ``quark exciton'') colorless state in QCD, which is formed by a single quark with its anti-quark image in the chromometallic mirror. Analogies with edge modes in topological insulators and boundary states of fractional vortices in multi-component condensates are highlighted.