Effective Potentials and Symmetry Restoration in the Chiral Abelian Higgs Model

Abstract

The chiral Abelian Higgs model is studied at finite temperature. By integrating out the heavy modes, we make a three-dimensional effective theory for the static modes. It is demonstrated that the plasma masses are correctly reproduced to leading order in $m^{2}/T^{2}$. The effective potential for the composite operator $\phi^{\dagger}\phi$ is calculated at one loop for the resulting three-dimensional theory and it is shown that the result is gauge parameter invariant. The numerical investigation of the potential reveals that the symmetry is restored via a first order phase transition. Comparison with the ordinary ring improved potential is made and it is found that the barrier height at $T_{c}$ is somewhat higher.