The lattice Landau gauge photon propagator for 4D compact QED

TL;DR

This study analyzes the Landau gauge photon propagator in 4D compact QED across confined and deconfined phases using large lattice volumes, revealing phase-dependent behaviors and topological effects.

Contribution

It provides the first detailed lattice computation of the photon propagator in 4D compact QED in both phases, highlighting the impact of topology and volume on the propagator and static potential.

Findings

In the confined phase, the propagator is finite and fits a Yukawa form.

In the deconfined phase, the propagator approaches that of a free field with increasing volume.

The static potential is linear in the confined phase and constant in the deconfined phase.

Abstract

In this work we report on the Landau gauge photon propagator computed for pure gauge 4D compact QED in the confined and deconfined phases and for large lattices volumes: $32^4$, $48^4$ and $96^4$. In the confined phase, compact QED develops mass scales that render the propagator finite at all momentum scales and no volume dependence is observed for the simulations performed. Furthermore, for the confined phase the propagator is compatible with a Yukawa massive type functional form. For the deconfined phase the photon propagator seems to approach a free field propagator as the lattice volume is increased. In both cases, we also investigate the static potential and the average value of the number of Dirac strings in the gauge configurations $m$. In the confined phase the mass gap translates into a linearly growing static potential, while in the deconfined phase the static potential approaches a constant at large separations. Results shows that $m$ is, at least, one order of magnitude larger in the confined phase and confirm that the appearance of a confined phase is connected with the topology of the gauge group.