Phase transitions and confinement in the Abelian Higgs model

Abstract

A lattice version of the Abelian Higgs model is studied in arbitrary Euclidean dimension. Two different representations of the theory, one in terms of the Higgs and gauge fields and the other in terms of the topological excitations, are used to understand what phases exist for the system. In addition to limiting cases there is, in two dimensions, a plasma phase of vortex excitations. The vortices (instantons) in this phase cause confinement (in the sense of Wilson) of fractional, but not integer, charges. In three and more dimensions, there is a plasma phase similar to the one in two dimensions as well as another phase which does not confine any charge. We argue that the confinement due to topological excitations in the plasma phase has the same physical basis as the usual large-coupling-constant (high temperature) confinement of the lattice gauge theory. Effects of a background field in two dimensions are also described.