Phase diagram of 3D SU(3) gauge-adjoint Higgs system

Abstract

Thermally reduced QCD leads to three dimensional SU(3) gaugefields coupled to an adjoint scalar field $A_0$. We compute the effective potential in the one-loop approximation and evaluate the VEV's of $Tr{A}_0^2$ and $Tr{A}_0^3$. 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. It is plausible that in the Higgs phase one has a transition for large enough Higgs selfcoupling to a region where $Tr{A}_0^3$ has no VEV and where the gaugesymmetry is broken maximally to $U(1)\times U(1)$.

Comments: Contributing paper to the proceedings of the 5th International Workshop on Thermal Field Theories and their Applications, Regensburg, Germany, August 10-14, 1998. Corrected typos, changes in wording