Domain Structures and Static Potentials in \(G_2\) Gauge Theory

Abstract

We investigate the domain structures of the \(G_2\) vacuum and the associated static potentials within the domain model, considering both zero and non-zero aggregate flux vacuum domains. Potentials associated with domains of zero aggregate flux exhibit favorable Casimir scaling and convexity properties at intermediate distances, and their long-range behavior matches the expected ordering of constant potential values according to representation. In contrast, potentials derived from domains with nonzero aggregate flux deviate from the key features of the confining force, as the absence of a minimal center-flux magnitude renders such configurations physically improbable. Furthermore, the potential ratios for \(SU(3)\) and \(SU(2)\) subgroups are found to be consistent with Casimir ratios of \(G_2\) at intermediate regimes, suggesting a possible role for these subgroups in the confinement mechanism of the \(G_2\) gauge group.

Comments: 13 pages, 7 figures