k-string tensions in the 4-d SU(N)-inspired dual Abelian-Higgs-type theory

TL;DR

This paper investigates k-string tensions in a 4-dimensional dual Abelian-Higgs model, deriving corrections to Casimir scaling and analyzing the effects of closed strings and monopole plasma non-diluteness.

Contribution

It provides explicit corrections to Casimir scaling in the dual Abelian-Higgs model and links these corrections to monopole plasma effects and closed string contributions.

Findings

Casimir scaling holds in the London limit without closed strings.

Explicit corrections to Casimir scaling are derived when including closed strings.

Casimir scaling persists at high monopole densities if the string world sheet is flat.

Abstract

The k-string tensions are explored in the 4-d $[U(1)]^{N-1}$-invariant dual Abelian-Higgs-type theory. In the London limit of this theory, the Casimir scaling is found in the approximation when small-sized closed dual strings are disregarded. When these strings are treated in the dilute-plasma approximation, explicit corrections to the Casimir scaling are found. The leading correction due to the deviation from the London limit is also derived. Its N-ality dependence turns out to be the same as that of the first non-trivial correction produced by closed strings. It also turns out that this N-ality dependence coincides with that of the leading correction to the k-string tension, which emerges by way of the non-diluteness of the monopole plasma in the 3-d SU(N) Georgi-Glashow model. Finally, we prove that, in the latter model, Casimir scaling holds even at monopole densities close to the mean one, provided the string world sheet is flat.