Instanton-Sphaleron transition in the d = 2 Abelian-Higgs model on a Circle

TL;DR

This paper investigates how the transition from quantum to classical regimes in the 2D Abelian-Higgs model on a circle varies with the circle's size, revealing both first- and second-order transitions.

Contribution

It demonstrates the existence of both sharp and smooth phase transitions in the compactified model, providing an analytically tractable prototype for studying baryon number violation.

Findings

Both first-order and second-order transitions occur depending on circle size.

The model can be analyzed analytically, aiding understanding of complex higher-dimensional cases.

Potential application to baryon number violating processes.

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 $S^1$. 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.