Domain walls and perturbation theory in high-temperature gauge theory: SU(2) in 2+1 dimensions

We study the detailed properties of $Z_2$ domain walls in the deconfined high-temperature phase of the $d=2+1\mathrm{}$ SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter $g^2/T$ is close to unity. The quantities studied include the surface tension, the action density profiles, roughening, and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-$T$ perturbation theory can be an accurate calculational tool.