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

We calculate the Euclidean action of a pair of Z2 monopoles (instantons), asa function of their spatial separation, in D=2+1 SU(2) lattice gauge theory. Wedo so both above and below the deconfining transition at T=Tc. At high T, andat large separation, we find that the monopole `interaction' grows linearlywith distance: the flux between the monopoles forms a flux tube (exactly like afinite portion of a Z2 domain wall) so that the monopoles are linearlyconfined. At short distances the interaction is well described by a Coulombinteraction with, at most, a very small screening mass, possibly equal to theDebye electric screening mass. At low T the interaction can be described by asimple screened Coulomb (i.e. Yukawa) interaction with a screening mass thatcan be interpreted as the mass of a `constituent gluon'. None of this isunexpected, but it helps to resolve some apparent controversies in the recentliterature.Comment: 14 pages, 2 figure