Phase diagram of 3D SU(3) gauge-adjoint Higgs system and C-violation in hot QCD

Thermally reduced QCD leads to three dimensional SU(3) gaugefields coupled to an adjoint scalar field A,. We compute the effective potential in the on e-loop approximation and evaluate the VEVs of TrA(2)(0) and TrA(3)(0). In t he Higgs phase not only the former, but also the latter has a VEV. This hap pens where the SU(3) gauge symmetry is broken minimally with U(2) still unb roken. The VEV of the cubic invariant breaks charge conjugation and CP. It is plausible that in the Higgs phase one has a transition for large enough Higgs selfcoupling to a region where TrA(3)(0) has no VEV and where the gau gesymmetry is broken maximally to U(1) x U(1). For a number of colours larg er than 3 an even richer phase structure is possible. (C) 1999 Elsevier Sci ence B.V. All rights reserved. PACS: 78.60.Mq; 43.35. fd; 95.75.Kk; 25.75.G z.