k-string tensions in the 3-d SU(N) Georgi-Glashow model

TL;DR

This paper investigates k-string tensions in the 3-dimensional SU(N) Georgi-Glashow model, showing that Casimir scaling holds at leading order and analyzing various corrections that affect this scaling, with implications for related gauge theories.

Contribution

It extends Polyakov's confinement argument to study k-string spectra, analyzing corrections to Casimir scaling in the 3-d SU(N) Georgi-Glashow model, including non-diluteness and Higgs field effects.

Findings

Casimir scaling holds at leading order in the weakly-coupled model.

Non-diluteness effects become significant when k is of order N.

Corrections from the Higgs field and closed k-strings modify the scaling ratio.

Abstract

The classic argument by Polyakov showing that monopoles produce confinement in the Higgs phase of the Georgi-Glashow model is generalized to study the spectrum of k-strings. We find that the leading-order low-density approximation yields Casimir scaling in the weakly-coupled 3-d SU(N) Georgi-Glashow model. Corrections to the Casimir formula are considered. When k is of the order of N, the non-diluteness effect is of the same order as the leading term, indicating that non-diluteness can significantly change the Casimir-scaling behavior. The correction produced by the propagating Higgs field is also studied and found to increase, together with the non-diluteness effect, the Casimir-scaling ratio. Furthermore, a correction due to closed k-strings is also computed and is shown to yield the same k-dependence as the one due to non-diluteness, but with the opposite sign and a nontrivial N-dependence. Finally, we consider the possible implications of our analysis for the SU(N) analogue of compact QED in four dimensions.