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

We calculate the euclidean action of a pair of ℤ 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 = T. 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 ℤ 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