Compact QED in Landau Gauge: a lattice gauge fixing case study

We derive different representations of compact QED fixed to 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 {\it quenched\/}, that is, the Faddeev-Popov determinant cancels them out and they do not influence correlation functions such as the photon propagator; (B)Dirac strings are responsible for the nonzero mass pole of the photon propagator. Since in $D=3+1$ the photon mass undergoes a rapid drop to zero at $β_c$, the deconfinement point, this result predicts that Dirac strings must be sufficiently dilute at $β> β_c$. Indeed, numerical simulations reveal that the string density undergoes a rapid drop to near zero at $β\sim β_c$.

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