Confinement for all couplings in a ${\mathbb{Z}}_2$ lattice gauge theory

Abstract

For a particular lattice gauge theory with ${\mathbb{Z}}_2$ gauge invariance there is confinement for all couplings. The gauge fields, on lattice links, lie in the closed interval $[-1,1]$. It is proved that the expectation value of a gauge-invariant loop operator decays as the exponential of minus the area.

Comments: Now 11 pages, AMSTEX. Small corrections, additional remarks, in particular on relation with lattice Yang-Mills theory. References revised. Published version