The photon propagator in compact QED_{2+1}: the effect of wrapping Dirac strings

TL;DR

This study investigates how closed Dirac strings affect the photon propagator in 2+1 dimensional compact QED, revealing that removing these strings resolves unphysical behaviors in the deconfinement phase.

Contribution

The paper demonstrates that closed Dirac strings cause unphysical photon propagator behavior and introduces a method to separate propagator measurements based on the number of thermal Dirac strings.

Findings

Dirac strings cause unphysical behavior in the photon propagator.

Removing Dirac strings restores the propagator to expected physical behavior.

The number of thermal Dirac strings correlates with the propagator's mass and anomalous dimension.

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 (D_T) in the deconfinement (high temperature) phase. We show how one can monitor the number N_3 of thermal Dirac strings which allows to separate the propagator measurements into N_3 sectors. The propagator in N_3 \neq 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 N_3. Consequently, in the N_3=0 sector the unphysical behavior of the D_T photon propagator is cured and the deviation from the free massless propagator disappears.