The Higgs field and the ultraviolet behaviour of the vortex operator in 2+1 dimensions

TL;DR

This paper investigates how the presence of a dynamical Higgs field affects the ultraviolet behavior of the vortex operator in 2+1 dimensional gauge theories, revealing different impacts in QED and Georgi-Glashow models.

Contribution

It provides a detailed one-loop analysis of the vortex operator's ultraviolet behavior in both 2+1D QED and Georgi-Glashow models with dynamical Higgs fields, highlighting model-dependent effects.

Findings

Higgs field causes power-like correction to vortex propagator in 2+1D QED.

In the Georgi-Glashow model, the Higgs field does not affect the vortex propagator at one loop.

Ultraviolet behavior in the Georgi-Glashow model is independent of Higgs mass when Higgs is heavy.

Abstract

We calculate the change in the ultraviolet behaviour of the vortex operator due to the presence of dynamical Higgs field in both 2+1 dimensional QED and the 2+1 dimensional Georgi-Glashow model. We find that in the QED case the presence of the Higgs field leads at the one loop level to power like correction to the propagator of the vortex operator. On the other hand, in the Georgi-Glashow model, the adjoint Higgs at one loop has no affect on the vortex propagator. Thus, as long as the mass of the Higgs field is much larger than the gauge coupling constant, the ultraviolet behaviour of the vortex operator in the Georgi-Glashow model is independent of the Higgs mass.