Monopole creation operators as confinement--deconfinement order parameters

TL;DR

This paper compares two monopole creation operators in the Abelian Higgs model, demonstrating both can serve as order parameters for the confinement--deconfinement transition, despite differences in their dependence on Dirac string length.

Contribution

It introduces and numerically compares a new monopole creation operator that overcomes Dirac string visibility issues in the old version, establishing both as effective phase transition indicators.

Findings

Both operators serve as order parameters for the phase transition.

The old operator's condensate depends on Dirac string length.

Fixing the Dirac string length allows the old operator to distinguish phases.

Abstract

We study numerically two versions of the monopole creation operators proposed by Frohlich and Marchetti. The disadvantage of the old version of the monopole creation operator is due to visibility of the Dirac string entering the definition of the creation operator in the theories with coexisting electric and magnetic charges. This problem does not exist for the new creation operator which is rather complicated. Using the Abelian Higgs model with a compact gauge field we show that both definitions of the monopole creation operator can serve as order parameters for the confinement--deconfinement phase transition. The value of the monopole condensate for the old version depends on the length of Dirac string. However, as soon as the length is fixed the old operator certainly discriminates between the phases with condensed and non--condensed monopoles.