RENORMALIZATION-GROUP STUDY OF THE MASSIVE SINE–GORDON THEORY AND PHASE STRUCTURE OF THE ABELIAN HIGGS MODEL

Abstract

Mapping the Abelian Higgs model to the massive sine–Gordon theory, the phase structure of the Abelian Higgs model is studied. The effect of interaction between instantons in the Abelian Higgs model is treated through the renormalization-group study of the massive sine–Gordon model. In the small dynamical-mass region the interaction between instantons is not negligible, and the effective density of instantons becomes very low at long distance (over the crossover distance) by the pairing mechanism. Therefore, the Abelian Higgs model reduces to a massive scalar theory interacting with very dilute instantons. In the large dynamical-mass region, the pairing mechanism of instanton and anti-instanton does not occur. This crossover phenomenon can be observed by the Wilson loop of a fractional charge. The relationship with the massive Schwinger–Thirring model is also discussed. It is also shown that the recently studied topological-field region is an ultraviolet fixed point of the renormalization-group flow.