Color-SU(3)-Ginzburg-Landau Effective Potential for Order Parameter with ${\bf 3} \times {\bf 3}$ Symmetry

Abstract

Ginzburg-Landau effective potential is studied for the order parameter that transforms in the $(3,3)$ representation under the color SU(3) group. All the SU(3) terms to the fourth-order of the order parameter are classified and the effective potential is constructed in its most general form. The conditions which stabilize the condensed phases are also obtained. As simple applications, the classification of the condensed phase is discussed in some special cases and the Higgs phenomenon associated with symmetry breaking is studied by introducing a coupling to the gauge boson.