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 A0. We compute the effective potential in the one-loop approximation and evaluate the VEVs of TrA02 and TrA03. In the Higgs phase not only the former, but also the latter has a VEV. This happens where the SU(3) gauge symmetry is broken minimally with U(2) still unbroken. 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 TrA03 has no VEV and where the gaugesymmetry is broken maximally to U(1)×U(1). For a number of colours larger than 3 an even richer phase structure is possible.