Lattice pure gauge compact QED in the Landau gauge: the photon propagator, the phase structure and the presence of Dirac strings

TL;DR

This study examines the lattice Landau gauge photon propagator and Dirac strings in compact QED, revealing their role in phase transitions, the presence of a mass gap in the confined phase, and the massless nature of the deconfined phase.

Contribution

It provides new insights into the topological structures and phase transition characteristics of compact QED through lattice simulations of the photon propagator and Dirac strings.

Findings

Confined phase has a finite photon propagator and a large number of Dirac strings.

Deconfined phase is massless with no Dirac strings and a diverging photon propagator at zero momentum.

The confinement-deconfinement transition is first order, identified by $eta$ dependence of observables.

Abstract

In this work we investigate the lattice Landau gauge photon propagator together with the average number of Dirac strings in the compact formulation of QED for the pure gauge version of the theory as a function of the coupling constant. Their $\beta$ dependence show that these two quantities can be used to identify the confinement-deconfinement transition and that the nature of this transition is first order. Our results show that in the confined phase the propagator is always finite, the theory has a mass gap and the number of Dirac strings present in the configuration is two orders of magnitude larger than in the deconfined phase. Furthermore, in the deconfined phase where $ \beta \ge 1.0125$ the theory becomes massless, there are essentially no Dirac strings and the photon propagator diverges when the limit $p \rightarrow 0^+$ is taken. Our results illustrate the importance of the topological structures in the dynamics of the two phases.