Monopole action from vacuum configurations in compact QED

TL;DR

This paper derives monopole actions from vacuum configurations in compact QED using Monte Carlo simulations, comparing different formulations and analyzing monopole condensation related to confinement.

Contribution

It extends Swendsen's method to derive monopole actions in compact QED, comparing Villain and Wilson formulations and analyzing monopole condensation.

Findings

Monopole action in Villain case agrees with dual transformation results

DeGrand-Toussaint monopole definition is useful for certain parameters

Monopole condensation occurs in the confinement phase in Wilson action

Abstract

It is possible to derive a monopole action from vacuum configurations obtained in Monte-Carlo simulations extending the method developed by Swendsen. We apply the method to compact QED both in the Villain and in the Wilson forms. The action of the natural monopoles in the Villain case is in fairly good agreement with that derived by the exact dual transformation. Comparing the monopole actions, we find (1) the DeGrand-Toussaint monopole definition may be useful for $\beta_V $ larger than about 0.5, (2) the Villain model well approximates the Wilson one for $\beta$ smaller than $\beta_c$ and (3) in the Wilson action the monopole condensation occurs in the confinement phase and $\beta_c$ may be explained by the energy-entropy balance of monopole loops like in the Villain case.