INSTANTON-SPHALERON TRANSITION IN THE d=2 ABELIAN–HIGGS MODEL ON A CIRCLE

Abstract

The transition from the instanton-dominated quantum regime to the sphaleron-dominated classical regime is studied in the d=2 Abelian–Higgs model when the spatial coordinate is compactified to S1. Contrary to the noncompactified case, this model allows both sharp first-order and smooth second-order transitions depending on the size of the circle. This finding may make the model a useful toy model for the analysis of baryon number violating processes. Since the model can to a large extent be treated analytically, it can also serve as a transparent prototype for the application of our method to more complicated cases, such as those in higher dimensions.