Z2 monopoles in D=2+1 SU(2) lattice gauge theory

TL;DR

This paper investigates the behavior of Z2 monopoles in 2+1 dimensional SU(2) lattice gauge theory, revealing their confinement properties and interaction types across different temperature regimes, thus clarifying recent debates.

Contribution

It provides a detailed calculation of monopole interactions at various temperatures, demonstrating linear confinement at high T and screened Coulomb interactions at low T, resolving previous controversies.

Findings

Monopoles exhibit linear confinement at high temperature.

At low temperature, interactions are described by a screened Coulomb potential.

The results clarify the nature of monopole interactions across the deconfining transition.

Abstract

We calculate the Euclidean action of a pair of Z2 monopoles (instantons), as a function of their spatial separation, in D=2+1 SU(2) lattice gauge theory. We do so both above and below the deconfining transition at T=Tc. At high T, and at large separation, we find that the monopole `interaction' grows linearly with distance: the flux between the monopoles forms a flux tube (exactly like a finite portion of a Z2 domain wall) so that the monopoles are linearly confined. At short distances the interaction is well described by a Coulomb interaction with, at most, a very small screening mass, possibly equal to the Debye electric screening mass. At low T the interaction can be described by a simple screened Coulomb (i.e. Yukawa) interaction with a screening mass that can be interpreted as the mass of a `constituent gluon'. None of this is unexpected, but it helps to resolve some apparent controversies in the recent literature.