On the Nature of the Abelian Higgs Model Phase Transition

The nature of the Abelian Higgs Model phase transition is investigated. A variational approximation is used in the evaluation of the relevant finite temperature effective potential. Some of the results presented are valid not only in the Abelian Higgs Model, but also in more complex theories. Several recent studies have been devoted to the phase transition of the Abelian Higgs Model. Besides being interesting in its own right, the Abelian Higgs Model gives a simple setting in which one can develop techniques that might be useful in the investigation of other gauge theories with spontaneous symmetry breaking. In this lecture I discuss a variational technique that can be used in the evaluation of the finite temperature effective potential, which is an important tool in the investigation of phase transitions. I illustrate this technique by studying the daisy and superdaisy resummed finite temperature effective potential of the Abelian Higgs Model. As discussed in Ref.8, using the composite operator method one can show that, if e < λ < e, the daisy and superdaisy resummed effective potential of the Abelian Higgs Model can be written as V res T = V res T (φ,G0) = − m 2 φ + λ 24 φ + 1 2 ∑ ∫ k lnG 0 (k) + 1 2 ∑ ∫ k [D(φ; k)G0(k)− 1] +V (a) 2 (G0) + V (b) 2 (G0) + V (c) 2 (G0) + V (d) 2 (G0) , (1) where V (a) 2 (G) ≡ − λ 4! ∑ ∫