Boundary states and non-Abelian Casimir effect in lattice Yang-Mills theory
M. N. Chernodub, V. A. Goy, A. V. Molochkov, Alexey S. Tanashkin
Abstract
Using first-principles 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 ${m}_{\mathrm{gt}}=\phantom{\rule{0ex}{0ex}}1.0(1)\sqrt{\ensuremath{\sigma}}=0.49(5)\text{ }\text{ }\mathrm{GeV}=0.29(3){M}_{{0}^{++}}$, which is substantially lighter than the ${0}^{++}$ ground-state glueball. We call this excitation ``glueton,'' interpreting it as a nonperturbative 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 antiquark image in the chromometallic mirror. Analogies with edge modes in topological insulators and boundary states of fractional vortices in multicomponent condensates are highlighted.