Photon propagator in compact (2+1)-dimensional QED: The effect of wrapping Dirac strings

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 leftover Dirac strings are responsible for the previously observed unphysical behavior of the propagator of spacelike photons (D_T) in the deconfinement (high temperature) phase. We show how one can monitor the number N₃ of thermal Dirac strings which allows us to separate the propagator measurements into N₃ sectors. The propagator in N₃≠0 sectors is characterized by a nonzero mass and an anomalous dimension similarly to the confinement phase. Both the mass squared and anomalous dimension are found to be proportional to N₃. Consequently, in the N₃=0 sector the unphysical behavior of the D_T photon propagator is cured and the deviation from the free massless propagator disappears.