Compact Qed in Landau Gauge: a Lattice Gauge Xing Case Study

We derive diierent representations of compact QED xed to Lan-dau gauge by the lattice Faddeev-Popov procedure. Our analysis nds that (A)Nielsen-Olesen vortices arising from the compactness of the gauge-xing action are quenched , that is, the Faddeev-Popov determinant cancels them out and they do not innuence 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 c , the deconnne-ment point, this result predicts that Dirac strings must be suuciently dilute at > c. Indeed, numerical simulations reveal that the string density undergoes a rapid drop to near zero at c .