2+1 Dimensional Georgi-Glashow Instantons in Weyl Gauge

TL;DR

This paper studies instanton solutions in the 3D SU(2) Georgi-Glashow model, transforming them into Weyl gauge to clarify their tunneling interpretation and regularize gauge singularities, while comparing their features to other gauge theories.

Contribution

It provides a detailed analysis of 3D Georgi-Glashow instantons in Weyl gauge, highlighting their tunneling interpretation and regularization, and discusses their spectral flow with fermions.

Findings

Instantons are transformed into Weyl gauge for better interpretation.

The model exhibits both instanton and sphaleron solutions, unlike other gauge theories.

Spectral flow analysis of fermions in instanton background is discussed.

Abstract

Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are transformed into the Weyl gauge. This illustrates the tunneling interpretation of these instantons and provides a smooth regularization of the singular unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak theory which has a sphaleron but no instantons. We also discuss the spectral flow picture of fundamental fermions in a Georgi-Glashow instanton background.