Compact QED in the Landau gauge: A lattice-gauge-fixing case study

We derive different representations of compact QED fixed to the Landau gauge by the lattice Faddeev-Popov procedure. Our analysis finds that (a) Nielsen-Olesen vortices arising from the compactness of the gauge-fixing action are quenched, that is, the Faddeev-Popov determinant cancels them out and they do not influence correlation functions such as the photon propagator, and (b) Dirac strings are responsible for the nonzero mass pole of the photon propagator. Since in D=3+1 dimensions the photon mass undergoes a rapid drop to zero at βc, the deconfinement point, this result predicts that Dirac strings must be sufficiently dilute at β>βc. Indeed, numerical simulations reveal that the string density undergoes a rapid drop to near zero at β∼βc.