First evidence for Casimir scaling in G(2) lattice gauge theory

Potentials between static quarks and antiquarks from a few lowest representations were evaluated in numerical simulations of 4-dimensional pure G${}_2$ lattice gauge theory at various couplings. The obtained potentials are linearly rising at intermediate distances and their string tensions exhibit (approximate) Casimir scaling. This result is in accordance with a model of the vacuum of non-Abelian gauge theories with a domain structure, in which the (color) magnetic flux randomly fluctuates within a domain, but the total flux in each domain is quantized in units of the gauge group center.