Confinement for all couplings in a ${\mathbb Z}_{2}$ lattice gauge theory

TL;DR

This paper proves that in a specific ${ m Z}_2$ lattice gauge theory, confinement occurs for all coupling strengths, with gauge-invariant loop operators exhibiting area-law decay.

Contribution

It establishes confinement for all couplings in a ${ m Z}_2$ lattice gauge theory and demonstrates exponential decay of loop operator expectations.

Findings

Confinement holds for all couplings in the model.

Loop operator expectations decay exponentially with area.

Gauge fields are confined within the interval [-1,1].

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.