The photon propagator in compact QED2+1: the effect of wrapping Dirac strings
Abstract
We discuss the influence of closed Dirac strings on the photon propagator in the Landau gauge emerging from a study of the compact U(1) gauge model in 2+1 dimensions. This gauge also minimizes the total length of the Dirac strings. Closed Dirac strings are stable against local gauge-fixing algorithms only due to the torus boundary conditions of the lattice. We demonstrate that these left-over Dirac strings are responsible for the previously observed unphysical behavior of the propagator of space-like photons (DT) in the deconfinement (high temperature) phase. We show how one can monitor the number N3 of thermal Dirac strings which allows to separate the propagator measurements into N3 sectors. The propagator in N3 ≠ 0 sectors is characterized by a non--zero mass and an anomalous dimension similarly to the confinement phase. Both mass squared and anomalous dimension are found to be proportional to N3. Consequently, in the N3=0 sector the unphysical behavior of the DT photon propagator is cured and the deviation from the free massless propagator disappears.
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