The spectrum of the three-dimensional adjoint Higgs model and hot SU(2) gauge theory

We compute the mass spectrum of the SU(2) adjoint Higgs model in 2+1 dimens ions at several points located in the (metastable) confinement region of it s phase diagram. We find a dense spectrum consisting of an almost unaltered repetition of the glueball spectrum of the pure gauge theory, and addition al bound states of adjoint scalars. For the parameters chosen, the model re presents the effective finite temperature theory for pure SU(2) gauge theor y in four dimensions, obtained after perturbative dimensional reduction. Co mparing with the spectrum of screening masses obtained in recent simulation s of four-dimensional pure gauge theory at finite temperature, for the low- lying states we find quantitative agreement between the full and the effect ive theory for temperatures as low as T = 2T(c). This establishes the model under study as the correct effective theory, and dimensional reduction as a viable tool for the description of thermodynamic properties. We furthermo re compare the perturbative contribution similar to gT with the non-perturb ative contributions similar to g(2)T and similar to g(3)T to the Debye mass . The latter turns out to be dominated by the scale g(2)T, whereas higher o rder contributions are small corrections. (C) 2000 Elsevier Science B.V. Al l rights reserved.